Ronald Brown (mathematician)

Ronald Brown

Ronald "Ronnie" Brown (born January 4, 1935 in London ) is a British mathematician who deals with topology and category theory. He is a professor at the University of Wales at Bangor .

Life

Brown studied at Oxford University with a bachelor's degree in 1956 and a doctorate in 1962 with JHC Whitehead (Some Problems in Algebraic Topology: Function Spaces and FD Complexes). From 1959 he was Assistant Lecturer and then Lecturer at the University of Liverpool , from 1964 Senior Lecturer and then Reader at the University of Hull and from 1970 Professor at the University of Wales in Bangor. From 1999 he held a research professorship and from 2001 he was Professor Emeritus, where he was a Leverhulme Fellow for the research project Crossed complexes and homotopy groupoids from 2002 to 2004 .

1983/84 he was visiting professor at the University of Strasbourg (with Jean-Louis Loday ).

He is not to be confused with the mathematician Ronald P. Brown , professor at the University of Hawaii.

plant

In the early 1960s, he dealt with the topology of functional spaces and the question of suitable ( convenient ) categories for their description, which established the research area convenient topology . This was also the subject of his dissertation and became known among topologists when it was picked up by Norman Steenrod in 1967 . In the 1980s he turned to groupoids in topology, about which he wrote a review article in 1987 (and even proposed to replace the name group in general with groupoid, since the former are only a special case). He pursues the reconstruction of the algebraic topology (homotopy theory) with higher dimensional groupoids and other techniques such as crossed complexes , which is presented in his book Nonabelian algebraic topology from 2011. Brown has been working on this with his school since the 1970s ( higher dimensional group theory , higher dimensional categories ). A central concern was the generalization of Seifert and van Kampen's theorem about fundamental groups with the help of gruppoids (about which Brown published in 1967 and what also happened in the other context of algebraic geometry in the Grothendieck seminar of the 1960s) and the proof of "higher-dimensional" versions of the sentence. As part of this, there was also an exchange with Alexander Grothendieck in the early 1980s, which led to his manuscript Pursuing Stacks .

Fonts

• Elements of Modern Topology, McGraw Hill, 1968
  • 2nd edition as: Topology: a geometric account of general topology, homotopy types, and the fundamental groupoid, Ellis Horwood, Chichester 1988
  • 3rd edition as: Topology and Groupoids, Booksurge LLC, 2006
• with Philip J. Higgins, Rafael Sivera: Nonabelian algebraic topology: Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids, EMS Tracts in Mathematics 15, 2011
• Editor with TL Thickstun: Low-Dimensional Topology, London Math. Soc. Lecture Notes No. 48, 1982 (Bangor Conference 1979)
• Ten topologies for , Quart. J. Math, Vol. 14, 1963, pp. 303-319 ${\displaystyle X\times Y}$
• Function spaces and product topologies, Quart. J. Math. Vol. 15, 1964, pp. 238-250.
• with Peter Booth: On the application of fibred mapping spaces to exponential laws for bundles, ex-spaces and other categories of maps, Gen. Top. Appl., Vol. 8, 1978, pp. 165-179.
• Groupoids and Van Kampen's theorem, Proc. London Math. Soc. (3), Vol. 17, 1967, pp. 385-401
• with PJ Higgins: On the connection between the second relative homotopy groups of some related spaces, Proc. London Math. Soc. (3), Vol. 36, 1978, 193-212.
• From groups to groupoids: a brief survey, Bull. London Math. Soc., Volume 19, 1987, pp. 113-134.
• with A. Al-Agl, R. Steiner: Multiple categories: the equivalence between a globular and cubical approach, Advances in Mathematics, Volume 170, 2002, pp. 71-118.
• 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, Fields Institute Communications, Volume 43, 2004, pp. 101-130

Web links

• Homepage in Bangor

Individual evidence

1. ↑ Ronald Brown in the Mathematics Genealogy Project (English)
2. ↑ Steenrod, A convenient category of topological spaces, Michigan Math. J. 14 (1967), 133-152
3. ↑ Som Naimpally, Convenient Topology, Topology Atlas
4. ↑ Convenient category of topological spaces, Ncat Lab
5. ↑ Nonabelian Algebraic Topology, Ncat Lab
6. ↑ Brown: Higher dimensional group theory ( memento of the original from January 1, 2012 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. 
7. ^ Brown, The origins of Alexander Grothendieck's Pursuing Stacks