bio | website | bangor.ac.uk/r.brown |
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location | ||
age | 79 | |
visits | member for | 4 years, 5 months |
seen | Oct 14 at 17:28 | |
stats | profile views | 3,763 |
As a result of giving courses at BSc and MSc level at Liverpool, I got involved in writing a text published as "Elements of Modern Topology" with McGraw Hill in 1968, and the 3rd edition is now available as "Topology and Groupoids" from amazon, see my web page. It was writing this book, and trying to clarify certain points, such as the fundamental group of the circle, that got mew into the area of groupoids; this suggested the area of higher groupoids; research on this got going in the 1970s, and has been a major area in my work, with fortunate collaborations with Chris Spencer (1971-73), Philip Higgins (1974-2005), and Jean-Louis Loday (1981-1985), and excellent contributions from research students.
Since 2001 I was engaged in writing a Tract giving an exposition in one place of my work since 1974 with Philip Higgins and a number of others on (strict) higher homotopy groupoids and their applications. A first step was to make available my out of print book on Topology, and this was made available in 2006 under the title "Topology and Groupoids" see my web page. The higher dimensional work was published in August, 2011, as a European Mathematical Society Tract, Vol 15, under the title "Nonabelian algebraic topology: filtered spaces, crossed complexes, cubical homotopy groupoids" with co-authors P.J. Higgins and R. Sivera.
Oct 13 |
comment |
General gluing theorem for adjunction spaces
I think the general result in a cofibration category is of interest but I would also like to know of significant topological examples where the closed hypothesis is dropped. If anyone wants to see the original proof it is available in this upload of Chapter 7 of Topology and Groupoids: pages.bangor.ac.ul/~mas010/pdffiles/TandGCh7.pdf |
Oct 2 |
revised |
Compelling evidence that two basepoints are better than one
gave a recent link |
Sep 28 |
awarded | Nice Answer |
Sep 24 |
awarded | Autobiographer |
Sep 12 |
awarded | Necromancer |
Sep 9 |
revised |
Naturality of a Kunneth formula for cohomology
typos |
Sep 9 |
answered | Naturality of a Kunneth formula for cohomology |
Sep 8 |
comment |
Decomposition vs filtration vs stratification
You should be interested in the comments of Grothendieck in section 5 of his "Esquisse d-un Programme" (1984) (matematicas.unex.es/~navarro/res/esquisseeng.pdf) which criticises the notion of topological space as inadequate for geometry, and discusses stratifications. See my preprint page pages.bangor.ac.uk/~mas010/brownpr.html for slides of a talk in June in Paris discussing the use of filtrations to define a strict cubical higher homotopy groupoid. |
Sep 1 |
revised |
Is there an accepted definition of $(\infty,\infty)$ category?
gave an additional link, and one typo corrected |
Aug 19 |
revised |
Do Disjoint Unions and Fiber Products Commute?
gave a link to a PhD thesis |
Aug 5 |
revised |
Generalized Categories for “Higher Homotopy Groupoids”
additional remarks, dated |
Jul 22 |
revised |
Why are we interested in the Fundamental Groupoid of a Space?
added a remark on exact sequences for fibrations of groupoids |
Jul 22 |
comment |
Compelling evidence that two basepoints are better than one
@HJRW: Just to show the value of a more general viewpoint, groupoids and higher van Kampen theorems led Loday and I to the notion of nonabelian tensor product of groups which act on each other; the current bibliography on my web page has 131 items, mainly from group theorists (only 5 with my name on). See also answers to mathoverflow.net/questions/175923. |
Jul 17 |
awarded | Nice Answer |
Jul 17 |
revised |
Why are we interested in the Fundamental Groupoid of a Space?
Three more significant uses of the fundamental groupoid |
Jul 14 |
revised |
Why are we interested in the Fundamental Groupoid of a Space?
typo |
Jul 14 |
revised |
Why are we interested in the Fundamental Groupoid of a Space?
added an extra point about the proof |
Jul 13 |
answered | Why are we interested in the Fundamental Groupoid of a Space? |
Jul 13 |
awarded | Nice Answer |
Jul 11 |
answered | How does one justify funding for mathematics research? |