last updated, October 5, 2014

 In 2013, Ronald Brown had 124 items on MathSciNet and was cited 998 times by 456 authors in the MR Citation Database.

This page contains a number of links to pdf and other files.

 Preprint page (includes articles not yet accepted or printed) and also beamer pdfs of seminars, etc.

Nonabelian algebraic topology :
filtered spaces, crossed complexes, cubical homotopy groupoids  by Ronald Brown, Philip J. Higgins, Rafael Sivera (description of new book: xxxv+668 pages, full pdf downloadable as hyperref e-book; EMS Tract vol 15, ISBN 978-3-13719-083-8, August 2011).
This gives a new foundation for algebraic topology, relying on a Seifert-van Kampen Theorem for the fundamental crossed complex of a filtered space, which allows new proofs of some classical theorems such as the Relative Hurewicz Theorem; it also allows new calculations of some nonabelian second relative homotopy groups, not available by traditional methods of singular homology and simplicial approximation. Indeed, it allows computation of some homotopy 2-types, based on calculations with crossed modules. Dealing with algebraic models of homotopy types requires a different approach to algebraic topology than the classical one.

Higher dimensional group theory  web article started 1996

Nonabelian tensor product of groups : this is a link to a bilbiography of 114 items on this topic, initiated in items [42] and [51].

Groupoids web article  

Articles on Popularisation and Teaching

Mathematics and Knots:  click here to see the sculptures of John Robinson and the exhibition Mathematics and Knots.

Home page

Ronald Brown PUBLICATIONS

DPhil Thesis: `Some problems in algebraic topology: a study of function space, function complexes, and FD-complexes' Submitted December, 1961. 140 pages . Part A, prelims, p. 1-28. 10.5MB
This Part contains the work on the cartesian closed category of Hausdorff k-spaces developed in [1,2], and also a brief exposition on what are now called monoidal closed categories.

Books


a. Elements of Modern Topology, McGraw Hill, Maidenhead, 1968 (out of print in 1972).
b. (coedited with T.L. Thickstun), Low-Dimensional Topology, (Volume 1 of the conference on Topology in Low Dimension, Bangor 1979), London Math. Soc. Lecture Notes No. 48 (1982). (this is now available again from CUP).
c. Topology: a geometric account of general topology, homotopy types, and the fundamental groupoid, Ellis Horwood, Chichester (1988) 460 pp. revised edition of (a). (out of print in 1992).
d.
Topology and Groupoids, Booksurge PLC, 2006, revised and updated edition of (c).
e. Nonabelian algebraic topology, with P.J. Higgins and R. Sivera (in press), EMS Tracts in Mathematics, vol 15.


Other output


(i) ``How mathematics gets into knots'', London Mathematical Society Popular Lectures Video Series, (1987) 50 min.
(ii) ``Mathematics and knots'', Exhibition of 16 A2 boards, designed by R.Brown, N.D.Gilbert, and T.Porter, Mathematics and Knots, Bangor, 1989. Exhibited at the Royal Society/ Joint Mathematical Council Pop Maths Roadshow, 1989-90; British Association for the Advancement of Science, Swansea, 1990; National Science Festival, Edinburgh, 1994.
(iii) ``Pivoted lines and the M\"{o}bius Band'', Computer Graphics Video, Storyline by R. Brown, Programming by Ramen Sen, Mathematics and Knots / IBM UK 4min. (1992).
(iv) ``Symbolic sculptures and mathematics'', World Wide Web Site
http://www.popmath.org.uk
Sculptures: John Robinson. Production: Cara Quinton. Mathematics: Ronald Brown. Edition Limit\'ee/ Centre for the Popularisation of Mathematics, 1996.
(v) ``Mathematics and knots'', World Wide Web Site
 http://www.popmath/exhib/ Centre for the Popularisation of Mathematics, 1997.
(vi) `Raising public awareness of mathematics':
CDRom, 2000, Version 1.1, 2001.

 

Papers


1. ``Ten topologies for $X\times Y$'', {\em Quart. J. Math.} (2) 14 (1963), 303-319. pdf
2. ``Function spaces and product topologies'', {\em Quart. J. Math.} (2) 15 (1964), 238-250. pdf
3. ``Cohomology with chains as coefficients'', {\em Proc. London Math. Soc.} (3) 14 (1964), 545-565. pdf file
4. ``On K\"{u}nneth suspensions'', {\em Proc. Camb. Phil. Soc.} 60 (1964) 713-720. pdf
5. ``The twisted Eilenberg-Zilber theorem'', {\em Celebrazioni Archimedi de secolo xx, Syracusa, 1964, Simposi di topologia } (1967) 33-37. pdf
6. ``On a method of P. Olum'', {\em J. London Math. Soc.} 40 (1965), 303-304. pdf
7. ``Two examples in homotopy theory'', {\em Proc. Camb. Phil. Soc.} 621 (1966) 575-576. pdf
8. ``Groupoids and Van Kampen's theorem'', {\em Proc. London Math. Soc.} (3) 17 (1967) 385-401. pdf
9. (with P.R. HEATH), ``Coglueing homotopy equivalences'', {\em Math. Z.} 113 (1970) 313-362. pdf
10. ``Fibrations of groupoids'', {\em J. Algebra} 15 (1970) 103-132. pdf   7.6MB
10a. ``The calculus and modern mathematics'', {\em Mathematics Teaching} 51 (1970) 6pp.
11. ``Groupoids as coefficients'', {\em Proc. London Math Soc.} (3) 25 (1972) 413-426.  pdf file
12. ``Sequentially proper maps and a sequential compactification'', {\em J. London Math Soc.} (2) 7 (1973) 515-522.  pdf file
13. (with G. DANESH-NARUIE), ``The fundamental groupoid as a topological groupoid'', {\em Proc. Edinburgh Math. Soc.} 19 (1975) 237-244. pdf
14. (with J.P.L. HARDY), ``Subgroups of free topological groups and free topological products of topological groups'', {\em J. London Math Soc.} (2) 10 (1975) 431-440. pdf
15. (with P.J. HIGGINS and S.A. MORRIS), ``Countable products of lines and circles: their closed subgroups, quotients and duality properties'', {\em Math. Proc. Camb. Phil. Soc.} 78 (1975) 19-32. pdf
16. ``Some non-projective subgroups of free topological groups'', {\em Proc. Amer. Math. Soc.} 52 (1975) 443-440. pdf
17. (with J.P.L. HARDY and S.A. MORRIS), ``The homotopy groups of an $n$-fold wedge'', {\em Math. Z.} 143 (1975) 119-121.
18. (with J.P.L. HARDY), ``Topological groupoids I: universal constructions'', {\em Math. Nachr.} 71 (1976) 273-286. pdf
19. (with G. DANESH-NARUIE and J.P.L. HARDY), ``Topological groupoids II: covering morphisms and $G$-spaces'', {\em Math. Nachr.} 74 (1976) 143-156. pdf
20. (with C.B. SPENCER), ``$\cal G$-groupoids, crossed modules and the fundamental groupoid of a topological group'', {\em Proc. Kon. Ned. Akad. v. Wet.} 7 (1976) 296-302. pdf
21. (with C.B. SPENCER), ``Double groupoids and crossed modules'', Cah. Top. G\'{e}om. Diff. 17 (1976) 343-362. pdf    pdferratum
22. (with P.J. HIGGINS), ``Sur les complexes crois\'es, $\omega$-groupo\"{\i}des et T-complexes'', {\em C.R. Acad. Sci. Paris S\'er. A.} 285 (1977) 997-999.  pdf
23. (with P.J. HIGGINS), ``Sur les complexes crois\'es d'homotopie associ\'es a quelques espaces filtr\'es'', {\em C.R. Acad. Sci. Paris S\'er. A.}286 (1978) 91-93. pdf
24. (with S.A. Morris), ``Embeddings in contractible or compact objects'', {\em Coll. Math.} 38 (1978) 193-212.
25. (with P.J. HIGGINS), ``On the connection between the second relative homotopy groups of some related spaces'', {\em Proc. London Math. Soc.} (3) 36 (1978) 193-212. pdf file
26. (with P.I. BOOTH), ``Spaces of partial maps, fibred mapping spaces and the compact-open topology'', {\em Gen. Top. Appl.} 8 (1978) 181-195.  pdf
27. (with P.I. BOOTH), ``On the application of fibred mapping spaces to exponential laws for bundles, ex-spaces and other categories of maps'', {\em Gen. Top. Appl.} 8 (1978) 165-179.  pdf
28. (with P. NICKOLAS), ``Exponential laws for topological categories, groupoids and groups and mapping spaces of colimits'', {\em Cah. Top. G\'eom. Diff.} 20 (1979) 179-198. pdf
29. (with A.M. ABD-ALLAH), ``A compact-open topology on partial maps with open domain'', {\em J. London Math Soc.} (2) 21 (1980) 480-486. pdf
30. ``On the second relative homotopy group of an adjunction space: an exposition of a theorem of J.H.C. Whitehead'', {\em J. London Math. Soc.} (2) 22 (1980) 146-152. pdf
31. (with P.J. HIGGINS), ``On the algebra of cubes'', {\em J. Pure Appl. Algebra} 21 (1981) 233-260. pdf
32. (with P.J. HIGGINS), ``Colimit theorems for relative homotopy groups'', {\em J. Pure Appl. Algebra} 22 (1981) 11-41. pdf
33. (with P.J. HIGGINS), ``The equivalence of $\omega$-groupoids and cubical $T$-complexes'', {\em Cah. Top. G\'eom. Diff.} 22 (1981) 349-370. pdf
34. (with P.J. HIGGINS), ``The equivalence of $\infty$-groupoids and crossed complexes'', {\em Cah. Top. G\'eom. Diff.} 22 (1981) 371-386. pdf
35. (with J. HUEBSCHMANN), ``Identities among relations'', in {\em Low dimensional topology}, London Math. Soc. Lecture Note Series 48 (ed. R. Brown and T.L. Thickstun, Cambridge University Press, 1982), pp. 153-202. pdf 8MB
36. ``Higher dimensional group theory'', in {\em Low dimensional topology}, London Math Soc. Lecture Note Series 48 (ed. R. Brown and T.L. Thickstun, Cambridge University Press, 1982), pp. 215-238.
37. (with P.J. HIGGINS), ``Crossed complexes and non-abelian extensions'', {\em Category theory proceedings, Gummersbach}, 1981, Lecture Notes in Math. 962 (ed. K.H. Kamps et al, Springer, Berlin, 1982), pp. 39-50.   pdf (6.1MB)
38. ``Non-abelian cohomology and the homotopy classification of maps'', in {\em Homotopie alg\'ebrique et algebre locale, Conf. Marseille-Luminy} 1982, ed. J.-M. Lemaire et J.-C. Thomas, Ast\'erisques 113-114 (1984), 167-172. pdf (1.2MB)
39. ``An introduction to simplicial $T$-complexes'', in {\em Esquisses Math.}, 32 (1982) 1-27. pdf (2.4MB)
40. (with P.R. HEATH and H. KAMPS), ``Groupoids and the Mayer-Vietoris sequence'', {\em J. Pure Appl. Alg.} 30 (1983) 109-129. pdf (4.3MB)
41. (with A. RAZAK), ``A van Kampen theorem for unions of non-connected spaces'', {\em Archiv. Math.} 42 (1984) 85-88. pdf
42. (with J.-L. LODAY), ``Excision homotopique en basse dimension'', {\em C.R. Acad. Sci. Paris S\'er.} I 298 (1984) 353-356. pdf
43. ``Coproducts of crossed $P$-modules: applications to second homotopy groups and to the homology of groups'', {\em Topology} 23 (1984) 337-345.  pdf
44. (with P.R. HEATH and K.H. KAMPS), ``Coverings of groupoids and Mayer-Vietoris type sequences'', {\em Categorical Topology, Proc. Conf. Toledo, Ohio, 1983}. (Heldermann Verlag, Berlin) (1984) 147-162. pdf
45. ``Some non-abelian methods in homotopy theory and homological algebra'', {\em Categorical topology: Proc. Conference Toledo, Ohio, 1983}, (ed. H.L. Bentley et al., Heldermann, Berlin, 1984), pp. 108-146.
46. (with S.P. HUMPHRIES), ``Orbits under symplectic transvections I'', {\em Proc. London Math. Soc.} (3) 52 (1986) 517-531. pdf file 3.2MB
47. (with S.P. HUMPHRIES), ``Orbits under symplectic transvections II: the case $K=\bf F_2$'', {\em Proc. London Math. Soc.} (3) 52 (1986) 532-556.  pdf file
48. (with P.J. HIGGINS), ``Tensor products and homotopies for $\omega$-groupoids and crossed complexes'', {\em J. Pure Appl. Alg.} 47 (1987) 1-33.  pdf
49. (with J.-L. LODAY), ``Homotopical excision, and Hurewicz theorems, for $n$-cubes of spaces'', {\em Proc. London Math. Soc.} (3) 54 (1987) 176-192. pdf
50. ``From groups to groupoids: a brief survey'', {\em Bull. London Math. Soc.} 19 (1987) 113-134. pdf
51. (with J.-L. LODAY), ``Van Kampen theorems for diagrams of spaces'', {\em Topology} 26 (1987) 311-334. pdf
52. (with D.L. JOHNSON and E.F. ROBERTSON), ``Some computations of non-abelian tensor products of groups'', {\em J. Algebra} 111 (1987) 177-202. pdf
53. (with P.R. HEATH), ``Lifting amalgamated sums and other colimits of groups and topological groups'', {\em Math. Proc. Camb. Phil. Soc.} 102 (1987) 273-280.
54. ``A non abelian tensor product of groups'', {\em Algebra-Tagung Halle 1986}, Wissensch. Beitr., 33, Martin-Luther Univ. Halle-Wittenberg, Halle-Saale, (1987) 59-72.
55.(with G.J. ELLIS), ``Hopf formulae for the higher homology of a group'', {\em Bull. London Math. Soc.} 20 (1988) 124-128.  pdf   erratum
56. ``Carpentry: a fable'', {\em Mathematical Intelligencer}, 11, no.4 (1989) 37. html
57. (with M. GOLASINSKI), ``A model structure for the homotopy theory of crossed complexes'', {\em Cah. Top. G\'eom. Diff. Cat}. 30 (1989) 61-82. pdf
58. ``Symmetry, groupoids, and higher dimensional analogues'', {\em Symmetry II}, ed. Istvan Hargittai, {\em Computers Math. Applic.} 17 (1989) 49-57.
59. (with N.D. GILBERT), ``Algebraic models of 3-types and automorphism structures for crossed modules'', {\em Proc. London Math. Soc.} (3) 59 (1989) 51-73.  pdf file
60. ``Triadic Van Kampen theorems and Hurewicz theorems'', {\em Algebraic Topology, Proc. Int. Conf. March 1988}, Edited M.Mahowald and S.Priddy, Cont. Math. 96 (1989) 39-57. pdf 5.5MB pdf .3MB revised
61. (with P.J. HIGGINS), ``Crossed complexes and chain complexes with operators'', {\em Math. Proc. Camb. Phil. Soc.} 107 (1990) 33-57. pdf
62. ``Some problems in non-Abelian homotopical and homological algebra'', {\em Homotopy theory and related topics, Proceedings Kinosaki, 1988}, ed. M. Mimura, Springer Lecture Notes in Math., 1418 (1990) 105-129. pdf
63. ``Conversations with John Robinson'' in {\em Symbolism: sculptures and tapestries}, by John Robinson, (Mathematics and Knots, Bangor, Wales) (1989) 2-29.
64. ``Why we made an exhibition'', in {\em Souvenir Guide to the Pop Maths Road Show}, Royal Society/ Joint Mathematics Council (1989) 10-12.
65. (with T.PORTER), ``Making a mathematical exhibition'', in {\em The popularization of mathematics}, edited A.G.Howson and J.-P. Kahane, ICMI Study Series, Cambridge University Press, (1990) 51-64. see http://pages.bangor.ac.uk/~mas010/icmi89.html
66. Review of {\em Algebraic homotopy}, by H.J.Baues, Cambridge University Press, 1988, 455pp, {\em Bull.American Math. Soc.} 23 (1990) 182-190.
67. (with T.PORTER), ``Mathematics in Context: a new course'', {\em For the Learning of Mathematics}, 10 (1990) 10-15.
68. ``$q$-perfect groups and universal $q$-central extensions'', {\em Publ. Mat. Univ. Auton. Barcelona} 34 (1990) 291-297. pdf
69. ``Local-to-global techniques, groupoids, and holonomy'', {\em Proceedings International Conference on the Calculus of Variations, Tbilisi Nov. 1989}.
70. ``Higher order symmetry'', {\em Proc. of Assiut First International Conference of Mathematics and Statistics, Assiut, Feb, 1990}, Part I, Algebra and Geometry, Ed. E.K.Al-Hussaini and A.M.Abou-El-Ela, University of Assiut, (1990), 25-44.
71. (with P.J.HIGGINS), ``The classifying space of a crossed complex'', {\em Math. Proc. Camb. Phil. Soc.} 110 (1991) 95-120. pdf
72. (with H.J.BAUES), ``On the relative homotopy groups of the product filtration and a formula of Hopf'', {\em J. Pure Appl. Algebra} 89 (1993) 49-61. pdf
73. Preface to {\em Combinatorial homotopy and four-dimensional complexes}, by H.J.Baues, pp x-xx, de Gruyter, Berlin, 1991.
74. ``Computing homotopy types using crossed $n$-cubes of groups'', {\em Adams Memorial Symposium on Algebraic Topology}, Vol 1, edited N. Ray and G Walker, Cambridge University Press, 1992, 187-210. pdf
75. (with M. E.-S. A.-F. AOF), ``The holonomy groupoid of a locally topological groupoid'', {\em Top. Appl.}, 47 (1992) 97-113. pdf
76. (with K.C.H.MACKENZIE), ``Determination of a double Lie groupoid by its core diagram'', {\em J. Pure Appl. Algebra}, 80 (1992) 237-272. pdf
77. (with JOHN ROBINSON), ``Borromean circles'', {\em Letter, American Math. Monthly}, April, (1992) 376-377.
78. ``Out of line'', {\em Royal Institution Proceedings}, 64 (1992) 207-243. pdf     html
79. (with J.ROBINSON), ``The Universe Series of Symbolic Sculptures'', in {\em Symbolic Sculptures}, by John Robinson, Edition Limite\'e, Carouge Geneve, (1992), 103-123.
80. ``The Waldegrave White Paper'', {\em London Math. Soc. Newsletter}, November, (1992).
81. (with T. PORTER), ``Why choose mathematics?'', in {\em Mathematics for the Future}, IMA and Hobson's Press, 1993, 1994, 1995).
82. (with O MUCUK), ``Covering groups of non-connected topological groups revisited'', {\em Math. Proc. Camb. Phil. Soc}, 115 (1994) 97-110. pdf
83. (with C.PRITCHARD), ``The third man's knotty problems'', {\em The Scottish Mathematical Council Journal}, 23 (1993) 62-66. pdf
84. ``Symbolic sculptures by John Robinson", {\em Bangor Tourist Guide}, Mathematics and Knots, 1993.
85. ``Higher order symmetry of graphs'', {\em Bull. Irish Math. Soc.} 32 (1994) 46-59. pdf
86. (with A.P.TONKS), ``Calculations with simplicial and cubical groups in AXIOM'', {\em J. Symbolic Computation}, 17 (1994) 159-179.
87. (with T.PORTER), ``The methodology of mathematics'', {\em Bulletin International Commission of Mathematical Instruction}, 37 (1994) 23-37.
88. (with O. MUCUK), ``The monodromy groupoid of a Lie groupoid'', {\em Cah. Top. G\'eom. Diff. Cat},36 (1995) 345-369. pdf
89. (with O. MUCUK), ``Foliations, locally Lie groupoids, and holonomy'', {\em Cah. Top. G\'eom. Diff. Cat}, 37 (1996) 61-71. pdf
90. (with T. PORTER), ``The methodology of mathematics'', {\em Math. Gazette}, 79, July (1995) 321-334.  {\em CUBO} 2 (2000) 85-100.
91. ``Representation and computation for crossed modules'', Proceedings {\em Cat\'egories, Algebres, Esquisses, Neo-esquisses}, Caen, 1994, 6pp.
92. (with C.D.WENSLEY), ``On finite induced crossed modules and the homotopy 2-type of mapping cones'', {\em Theory and Applications of Categories} 1(3) (1995) 54-71.pdf
93. ``Homotopy theory, and change of base for groupoids and multiple groupoids'', {\em Applied categorical structures}, 4 (1996) 175-193. pdf
94. (with M. GOLASINSKI, T.PORTER and A.P.TONKS), ``Spaces of maps into classifying spaces for equivariant crossed complexes,'' {\em Indag. Mathem.}, 8 (1997) 157-172. pdf    pdfcorr
95. (with C.D.WENSLEY), ``Computing crossed modules induced by an inclusion of a normal subgroup, with applications to homotopy 2-types'', {\em Theory and Applications of Categories} 2 (1996) 3-16. pdf

96. (with G.JANELIDZE), ``Van Kampen theorems for categories of covering morphisms in lextensive categories'', {\em J. Pure Appl. Algebra} 119 (1997) 255-263. pdf
97. (with T. PORTER), ``On the Schreier theory of non-abelian extensions: generalisations and computations'', {\em Proceedings Royal Irish Academy}, 96 (1996) 213-227. pdf
98. (with G.JANELIDZE), "Galois theory of second order covering maps of simplicial sets", J. Pure Applied Algebra, 135 (1999) 83-91.pdf
99. `What should be the output of mathematical education?', in {\em Mathematics Education as a research domain: a search for identity}, edited Kilpatrick, J., Sierpinska, A., Kluwer, Lancaster, 1997, 459-476.
100. (with T.PORTER), "Matematikos metodologia", Alfa + Omega, 1 Nr 5 (1998) 71-84 (Lithuanian translation of `The Methodology of Mathematics', Formally, "Alpha+omega" is a supplement of the "Lithuanian Mathematical Journal", which has an ISSN number 0132--2818.)
101. `Mathematics and knots', in Visual Representations and Interpretations, Ray Paton and Irene Nielson (Eds), Springer-Verlag London 1999, 32-42. [translated into Lithuanian as `Matematika ir mazgai', "alpha + omega", No.2 (6) (1998) 5-14. pdf
102. `Groupoids and crossed objects in algebraic topology', Homology, homotopy and applications', 1 (1999) 1-78.    pdf (revised hyperref version)
103. `Nusos, matematiques i art', Butll. de la Soc. Catalana d. Matematiques, 13 (1998) 7-19. [Translated into Catalan by Gemma Bastardas from an article `Knots, mathematics and art' published in English in the Actes del VI Congres de Llenguatges Naturels i Llenguatges Formals (Tarragona, 17-21 Sept, 1990).]
104. (with A. RAZAK SALLEH), ``Free crossed crossed resolutions of groups and presentations of modules of identities among relations'' , London Math. Soc. J. Computation and Math. (2) (1999) 28-61. pdf
105.  (with G.H. MOSA) `Double categories, 2-categories, thin structures and connections', Theory and Applications of Categories, (1999), 163-175.
106. `John Robinson's Symbolic Sculptures, knots and mathematics', Proceedings ISAMA99, Ed N. Friedman and J. Barrallo, University of the Basque Country (san Sebastian) 1999, 75-82.
107. (with A. Heyworth) `Using rewriting systems to compute left Kan extensions and induced actions of categories', J. Symbolic Computation 29 (2000) 5-31. pdf
108. `Dismay and decadence in British Universities', letter to{\em Science \& Public Affairs}, August, 1999, p. 28.
109. `Mathematical themes in the sculptures of John Robinson  : 1 Borromean sculptures' Mathematics Today 36 (1) (2000) 6-7.
110. Review of `History of Topology' ed I M James, {\em London Math Soc. Newsletter}, Jan 2000, 25-27. pdf
111. (with T. Porter) `Mathematical Structure: Knowledge, Representation and Interpretation', in  Theoria et Historia Scientiarum, the International Journal of Interdisciplinary Studies, special issue on `Knowledge: representations and interpretations', edited W. Meyer and R. Paton. 6 (2002) 39-54.
112. `The symbolic sculptures of John Robinson', in  Theoria et Historia Scientiarum, the International Journal of Interdisciplinary Studies, issue on `Knowledge: representation and interpretation.', edited W. Meyer and R. Paton, 6 (2002) 55-73.
113. (with I. I\c cen ), 'Locally Lie subgroupoids and their Lie holonomy and monodromy groupoids', {\it Top. and its Appl.} 115 (2000) 125-138. pdf
113a.`Mathematical themes in the sculptures of John Robinson : 2 Polyhedra' Mathematics Today 36 (6) (2000) 172-173.

114. (with M. GOLASINSKI, T.PORTER and A.P.TONKS), ``Spaces of maps into classifying spaces for equivariant crossed complexes, II: The general topological group case.'' K-theory 23  (2001) 129-155. pdf
115. (with \.I. \.I\c cen ), `Homotopies and automorphisms of crossed modules of groupoids', Applied Categorical Structures, 11
(2003) 185-206.
pdf
116. (with F. A. Al-Agl and R. STEINER), ``Multiple categories: the equivalence of a globular and a cubical approach'', Advances in Mathematics 170 (2002) 71-118.  pdf
117. (with T. PORTER), ``The methodology of mathematics'', European Mathematical Society Newsletter June (2001) 12-14, Sept. (2001) 14-16.
118.(with K.HARDIE, H.KAMPS, T. PORTER), `` The homotopy double groupoid of a Hausdorff space'', Theory and Applications of Categories, 10 (2002) 71-93.
119. (with I.ICEN and O. MUCUK) `Holonomy and monodromy groupoids', in Lie Algebroids, Banach Center Publications Institute of Mathematics, Polish Academy of Sciences, Warsaw, 54 (2001) 9-20. pdf
120. `Algebraic homotopy', Supplement III Encyclopaedia of Mathematics Managing Editor: M. Hazewinkel Kluwer Academic Publishers (2002) 29-31.
121. `Exponential law in topology', Supplement III Encyclopaedia of Mathematics Managing Editor: M. Hazewinkel Kluwer Academic Publishers (2002) 142-143.
122. (with \.I. I\c{c}en, and O. Mucuk), `Examples and coherence properties of local subgroupoids', Topology and its Applications 127 (2003) 393-408.
123. (with I.ICEN) `Towards a 2-dimensional notion of holonomy', Advances in Math. 178 (2003) 141-175. pdf
124. (with C.D.WENSLEY), `Computation and homotopical applications of induced crossed modules', J. Symbolic Computation 35 (2003) 59-72. pdf
125. (with M. BULLEJOS and T.PORTER), `Crossed complexes, free crossed resolutions and graph products of groups', Proceedings Workshop Korea 2000, Heldermann Verlag. 27 (2003) 11-26. pdf
126. (with E. MOORE, T.PORTER, C.D.WENSLEY), `Crossed complexes, and free crossed resolutions for amalgamated sums and HNN-extensions of groups', UWB Math Preprint 02-09. math.AT/0207037 Georgian Math. J. 9 (2002) 623-644. pdf
127. `Serie di sculture simboliche dell'universo di John Robinson', in {\em Matematica, arte, tecnologia, cinema}, edited Michele Emmer, Mirella Manaresi, Springer-Verlag Italia, Milano, 2002, 19-30.
128.  `Forum discussion', in Mathematics and Art,: Mathematical Visualisation in Art and Education, Editor Claude P . Bruter, Springer-Verlag (Berlin Heidelberg) 2002, 155-159.
129. (with G. JANELIDZE), `Galois Theory and a new homotopy double groupoid of a map of spaces', Applied Categorical Structures 12 (2004) 63-80. pdf
130. (with T. PORTER), `The intuitions of higher dimensional algebra for the study of structured space', Revue de Synthèse, 124 (2003)  173-203. ` UWB Math. Preprint (pdf file).
131. (with HIGGINS, P.J.), `Cubical abelian groups with connections are equivalent to chain complexes', Homology, Homotopy and Applications, 5(1) (2003) 49-52.
132. `Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional local-to-global problems', Proceedings of the Fields Institute Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories, September 23-28, 2002, Fields Institute Communications 43 (2004) 101-130. pdf of revised version
133. `Les escultures simb\`oliques de John Robinson', M\`etode, Universitat de Valencia, Revista de Difusi\'o de la Investigaci\'o, Primavera 2003, no. 37, 67-71.
134. (with J.F. Glazebrook), `Connections, local subgroupoids, and a holonomy Lie groupoid of a line bundle gerbe', Univ. Iagel. Acta Math. XLI (2003) 283-296 (UWB Math Preprint 02.22).
135. (with H.B. Griffiths) `Obituary: W.H. Cockcroft', Bull. London Math. Soc. 37 (2005) 149-155.
136. (with T. Porter), `Category theory and higher dimensional algebra: potential descriptive tools in neuroscience', Proceedings of the International Conference on Theoretical Neurobiology, Delhi, February 2003, edited by Nandini Singh, National Brain Research Centre, Conference Proceedings 1 (2003) 80-92. pdf
137. (with R.Paton and T. Porter),  `Categorical language and hierarchical models for cell systems', Computation in Cells and Tissues - Perspectives and Tools of Thought, Paton, R.; Bolouri, H.; Holcombe, M.; Parish, J.H.; Tateson, R. (Eds.) Natural Computing Series, Springer (2004) 289-303. pdf
138. `$k$-spaces', in Encyclopedia of General Topology, ed. K.P.Hart, J. Nagata, and J.E. Vaughan, Elsevier (2004) 189-191. pdf
139. (with N. Ghani, A.Heyworth, C.D.Wensley), `String rewriting systems for double coset systems', J. Symb. Comp. 41 (2006) 573-590.UWB Math Preprint 04.04. arXiv:math/0508391
140. (with H. Kamps and T. Porter), `A homotopy double groupoid of a Hausdorff space II: a van Kampen theorem', Theory and Appl. Cat.14, (2005) 200-220.
141. `John Robinson's Symbolic Sculptures: Knots and mathematics', in `The visual mind II', edited Michele Emmer, MIT Press, (2005) 125-139.
142. `Mathematicians struggle for truth', Letter to the Independent, Aug 17, 2005.
143. `Allow beautiful minds to thrive', letter in the Times HigherEducational Supplement, September 16, 2005.
144. `Origins of Grothendieck's Pursuing Stacks', Letter, Notices American Math. Soc., 52 (8) Sept, 2005, 830.
145. (with I. C. Baianu, G. Georgescu, and J. F. Glazebrook), `Complex nonlinear biodynamics in categories: higher dimensional algebra, and Lukasiewicz--Moisil Topos: transformations of neuronal, genetic and neoplastic networks', Axiomathes 16 (2006) 65-122.      
146. (with T. Porter) `Category Theory: an abstract setting for analogy and comparison', In: What is Category Theory? Advanced Studies in Mathematics and Logic, Polimetrica Publisher, Italy, (2006) 257-274. pdf
147. `Three themes in the work of Charles Ehresmann: Local-to-global; Groupoids; Higher dimensions', Proceedings of the 7th Conference on the Geometry and Topology of Manifolds: The Mathematical Legacy of Charles   Ehresmann, Bedlewo (Poland) 8.05.2005-15.05.2005, Banach Centre Publications 76, Institute of Mathematics Polish Academy of Sciences, Warsaw, (2007) 51-63. (math.DG/0602499).
pdf
148. (with Bak, A., Minian, G., and Porter, T.), `Groupoid atlases: an Introduction', abstract of talk to the `Colloque International: Charles Ehresmann: 100 ans', Amiens 7-9 October, 2005, Cah. Top. G\'eom. Diff. Cat. 46 (2005) 183.
149. (with Bak, A., Minian, G., and Porter, T.), `Global actions, groupoid atlases and applications', J. Homotopy and Related Structures, 1 (2006) 101-167. pdf
150. (with T. Porter), `Analogy, concepts and methodology in mathematics', Eureka, (September 2006) 23-27. UWB Math Preprint 06.08. pdf
151. `Groupoids, the Phragmen-Brouwer property and the Jordan curve theorem',  J. Homotopy and Related Structures 1 (2006) 175-183. arXiv:math/0607229  pdf
152. (with R. Sivera), `Normalisation for the fundamental crossed complex of a simplicial set',
J. Homotopy and Related Structures, Special Issue devoted to the memory of Saunders Mac Lane, 2 (2007)  49-79. math.AT/0611728 . pdf
153. `Promoting Mathematics', MSOR Connections 7 no 2 July 2007 21-25.
pdf
154. `John Robinson Sculptor, May 5 1935-April 6, 2007', Hyperseeing, June 2007, 3-7.
pdf
155. `John Robinson, The Sculptor', LMS Newsletter, July 2007, p.8. pdf
156. (with I. C. Baianu  and J. F. Glazebrook), ` Categorical Ontology of Complex Space-Time Structures: The Emergence of Life and Human Consciousness', Axiomathes,  17:  (2007)  223-352. pdf                                                 
 
157. (with I. C. Baianu and J. F. Glazebrook), `A Conceptual Construction for Complexity Levels Theory in SpaceTime Categorical Ontology: Non-Abelian Algebraic Topology, Many-Valued Logics and Dynamic Systems', Axiomathes , 17 (2007) .   pdf 
158. (with I. C. Baianu and J. F. Glazebrook),  `A Non--Abelian Categorical Ontology and Higher Dimensional Algebra of Spacetimes and Quantum Gravity'.  Axiomathes , 17 (2007) 353-408    pdf
159  (with I. C. Baianu and J. F. Glazebrook),  CATEGORICAL ONTOLOGY OF COMPLEX SYSTEMS, META--SYSTEMS AND LEVELS: The Emergence of life, Human Consciousness
and Society'.  In: ``Theory and Applications of Ontology." vol.1, R. Poli, et al., eds. 2008, Springer: Berlin (in press).
160. `Remembering George Mackey', Letter,  Notices American Mathematical Society, 54 no.10 , November, 2007, p.1280. 
161. `Mathoetic mode', Newsletter, London Mathematical Society, January 2008, p.26. html
162. `A new higher homotopy groupoid: the fundamental globular omega-groupoid of a filtered space', Homotopy, homology and applications, 10 (2008), No. 1, pp.327-343. pdf
163. with I. Morris, J. Shrimpton and C.D. Wensley, `Graphs of Morphisms of Graphs', Electronic Journal of Combinatorics, A1 of Volume 15(1), 2008. 1-28. pdf
164. `Exact sequences of fibrations of crossed complexes, homotopy classification of maps, and nonabelian extensions of groups', J. Homotopy and Related Structures 3 (2008) 331-343. pdf
165. `Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional local-to-global problems', in Michiel Hazewinkel (ed.), Handbook of Algebra, volume 6, Elsevier, 2009, p. 83-124. (revised version of [132] available as math.AT/0212274 v7). pdf
166. `Memory evolutive systems', Axiomathes, 19 (2009) 271-280. (Review of book by A-C. Ehresmann and J.P. Vanbremeersch). pdf
167. I.C. Baianu, J.F. Glazebrook and R. Brown, `Algebraic topology foundations of supersymmetry and symmetry breaking in quantum field theory and quantum gravity: a review' SIGMA (Symmetry, Integrability, and Geometry: Methods and Applications) 79 pp. pdf
168. R. Brown and R. Sivera, `Algebraic colimit calculations in homotopy theory using fibred and cofibred categories',  Theory and Applications of Categories, 22 (2009) 222-251 . pdf
169. `Promoting mathematics', EMS Newsletter, June 2010, 17-21. pdf of whole issue    pdf of article
170. `Possible connections between whiskered categories and groupoids, Leibniz algebras, automorphism structures and local-to-global questions', J. Homotopy and Related Structures, 5(1) (2010) 305-318. pdf
171. R. Brown and R. Street, `Covering morphisms of crossed complexes and of cubical omega-groupoids are closed under tensor product', Cah. Top. Geom. Diff. Cat., 52 (2011) 188-208. pdf
172. `Erratum to ``Possible connections between whiskered categories and groupoids, Leibniz algebras, automorphism structures and local-to-global questions ", vol.5 (1) 2010, pp.305-318.' J. Homotopy and Related Structures (2011) (to appear). pdf
173. with I. Baianu and J. Glazebrook, ``Quantum Symmetries, Operator Algebra and Quantum Groupoid Representations: Paracrystalline Systems, Topological Order, Supersymmetry and Global Symmetry Breaking", International Journal of Research and Reviews in Applied Sciences, 9, Issue 2 (November, 2011) 163--206. pdf
174. with T. Porter, ``What should be the context of an adequate specialist undergraduate education in mathematics?'', The De Morgan Journal 2 no. 1, (2012) 411--67. pdf
175. with J. Glazebrook, ``A Career of Unyielding Exploration: In Memory of Ion C. Baianu (19472013)", Quanta, (2) No 1 (2013) 1--6. html pdf
176. with O.A. Camarena, ``Corrigendum to ``Groupoids, the Phragmen-Brouwer Property, and the Jordan Curve Theorem'', J. Homotopy and Related Structures 1 (2006) 175-183.'' J. Homotopy and Related Structures (to appear) pdf

Rough Analysis of types of output

Papers on teaching: 10a, 56, 67, 80, 81, 87, 90, 99, 100, 153, 169, 174.

Papers on Popularisation: 63, 64, 65, 77, 79, 83, 101, 103, 106, 108, 117, 127, 128, 133, 161.

General expositions: 58, 78, 111, 112, 135, 136

Research Papers: The rest.

 

 Papers in preparation

P2. (with C.D.WENSLEY), ``On sorting sequences''.

Book in preparation

1. (with P.J. HIGGINS and   R.SIVERA)  `Nonabelian algebraic topology.

02.25 BROWN, R. & HIGGINS, P.J.
The fundamental groupoid of the quotient of a Hausdorff space by a discontinuous action of a discrete group is the orbit groupoid

 

Preprints not yet published

82.2 ``Holonomy and monodromy groupoids'', U.C.N.W. Pure Math. Preprint 82.2, 10pp.
86.4 ``A convenient category of topological spaces: historical note'', U.C.N.W. Pure Math. Preprint 86.4, 3pp.
88.11 (with G.H.MOSA), ``Double categories, $R$-categories, and crossed modules'', U.C.N.W. Mathematics Preprint 88.11, 13pp.
89.12 (with N.D. GILBERT and J. SHRIMPTON), ``Symmetry objects in closed categories'', 24pp.
90.23 ``The sculptures of John Robinson'', 9pp.
91.14 (with N.D.GILBERT, H.-J.HOEHNKE and J.SHRIMPTON), ``Non-Abelian tensor products of groups; groupoids; quadratic forms; and higher order symmetry'', 53pp, UCNW Math Preprint 91.14.

To Ronald Brown's Offprint/Preprint page

Escape routes

Back to Ronald Brown's Homepage

Back to Mathematics Homepage

View My Stats