last updated, April 19, 2008

 

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

 

Ronald Brown PUBLICATIONS

Books


a. Elements of Modern Topology, McGraw Hill, Maidenhead, 1968.
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).
c. Topology: a geometric account of general topology, homotopy types, and the fundamental groupoid, Ellis Horwood, Chichester (1988) 460 pp.
d.
Topology and Groupoids, Booksurge PLC, 2006.


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.
2. ``Function spaces and product topologies'', {\em Quart. J. Math.} (2) 15 (1964), 238-250.
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.
5. ``The twisted Eilenberg-Zilber theorem'', {\em Celebrazioni Archimedi de secolo xx, Syracusa, 1964, Simposi di topologia } (1967) 33-37.
6. ``On a method of P. Olum'', {\em J. London Math. Soc.} 40 (1965), 303-304.
7. ``Two examples in homotopy theory'', {\em Proc. Camb. Phil. Soc.} 621 (1966) 575-576.
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.
10. ``Fibrations of groupoids'', {\em J. Algebra} 15 (1970) 103-132.
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.
13. (with G. DANESH-NARUIE), ``The fundamental groupoid as a topological groupoid'', {\em Proc. Edinburgh Math. Soc.} 19 (1975) 237-244.
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.
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.
16. ``Some non-projective subgroups of free topological groups'', {\em Proc. Amer. Math. Soc.} 52 (1975) 443-440.
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.
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.
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.
21. (with C.B. SPENCER), ``Double groupoids and crossed modules'', Cah. Top. G\'{e}om. Diff. 17 (1976) 343-362.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
39. ``An introduction to simplicial $T$-complexes'', in {\em Esquisses Math.}, 32 (1982) 1-27.
40. (with P.R. HEATH and H. KAMPS), ``Groupoids and the Mayer-Vietoris sequence'', {\em J. Pure Appl. Alg.} 30 (1983) 109-129.
41. (with A. RAZAK), ``A van Kampen theorem for unions of non-connected spaces'', {\em Archiv. Math.} 42 (1984) 85-88.
42. (with J.-L. LODAY), ``Excision homotopique en basse dimension'', {\em C.R. Acad. Sci. Paris S\'er.} I 298 (1984) 353-356.
43. ``Coproducts of crossed $P$-modules: applications to second homotopy groups and to the homology of groups'', {\em Topology} 23 (1984) 337-345.
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.
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
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. erratum
56. ``Carpentry: a fable'', {\em Mathematical Intelligencer}, 11, no.4 (1989) 37.
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.
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.
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.
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.
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.
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.
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.
89. (with O. MUCUK), ``Foliations, locally Lie groupoids, and holonomy'', {\em Cah. Top. G\'eom. Diff. Cat}, 37 (1996) 61-71.
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.
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.
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.
96. (with G.JANELIDZE), ``Van Kampen theorems for categories of covering morphisms in lextensive categories'', {\em J. Pure Appl. Algebra} 119 (1997) 255-263.
97. (with T. PORTER), ``On the Schreier theory of non-abelian extensions: generalisations and computations'', {\em Proceedings Royal Irish Academy}, 96 (1996) 213-227.
98. (with G.JANELIDZE), "Galois theory of second order covering maps of simplicial sets", J. Pure Applied Algebra, 135 (1999) 83-91.
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
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.
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.
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', Proceedingsof 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.
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

 Preprint page (not yet accepted or printed)

Nonabelian algebraic topology  (download Part I)

 

Preprints 

Normalisation for the fundamental crossed complex of a simplicial set arXiv:math/0611728 [ps, pdf, other]
Authors: Ronald Brown, Rafael Sivera
A new higher homotopy groupoid: the fundamental globular omega-groupoid of a filtered space arXiv:math/0702677 [ps, pdf, other]

Possible connections between whiskered categories and groupoids, many object Lie algebras, automorphism structures and local-to-global questions arXiv:0708.1677 [ps, pdf, other]

Rough Analysis of types of output

Papers on teaching: 10a, 56, 67, 80, 81, 87, 90, 99, 100

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

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.

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