bio | website | bangor.ac.uk/r.brown |
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location | ||
age | 80 | |
visits | member for | 5 years, 1 month |
seen | 2 mins ago | |
stats | profile views | 4,465 |
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.
Jun 24 |
revised |
Higher refinement of Seifert-van Kampen theorem on the language of hocolim
deleted repetition |
Jun 24 |
comment |
Higher refinement of Seifert-van Kampen theorem on the language of hocolim
Lurie's version is also discussed at mathoverflow.net/questions/102295/… My answer below explains more on my ideas of such higher Seifert-van Kampen theorems. |
Jun 24 |
revised |
Higher refinement of Seifert-van Kampen theorem on the language of hocolim
added an abstract of the Aveiro presentation |
Jun 20 |
revised |
Higher refinement of Seifert-van Kampen theorem on the language of hocolim
extra explanation of history |
Jun 20 |
answered | Higher refinement of Seifert-van Kampen theorem on the language of hocolim |
Jun 10 |
revised |
Compelling evidence that two basepoints are better than one
added a link |
Jun 8 |
comment |
What is the intuition of connections for cubical sets?
Vezzani (arXiv:1405.4508) and cited papers there for relevance to motivic theory. In this area the corresponding simplicial methods have disadvantages! See also 116. (with F.A. AL-AGL and R. STEINER), `Multiple categories: the equivalence between a globular and cubical approach', Advances in Mathematics, 170 (2002) 71-118. |
Jun 8 |
comment |
What is the intuition of connections for cubical sets?
I'll add a couple of later references. Homology Homotopy Appl. Volume 14, Number 1 (2012), 133-158. Cubical approach to derived functors Irakli Patchkoria |
Jun 7 |
comment |
Pull-back of a fibration along a homotopy equivalence and homotopy classes of sections
You can contact me by email if you want. One seems to need the old trick: if abc is defined in a category, and ab, bc are isomorphisms, then a,b,c, are iso also. |
Jun 6 |
revised |
Pull-back of a fibration along a homotopy equivalence and homotopy classes of sections
added a comment on further studies of maps |
Jun 6 |
revised |
Pull-back of a fibration along a homotopy equivalence and homotopy classes of sections
added a reference |
Jun 6 |
answered | Pull-back of a fibration along a homotopy equivalence and homotopy classes of sections |
May 30 |
comment |
Is there a (satisfying) proof that cellular cohomology is isomorphic to simplicial cohomology that doesn't use relative cohomlogy?
@Andy Putnam The question asked in the last paragraph of the main question seems to be about the whole structure of the usual homology theory, starting with singular theory, and continuing with computation via cellular chains. One also has to look at the whole history of algebraic topology, as glimpsed in the book and presentation cited by me. These show a direct and homotopically defined way to the cellular complex, but in a more powerful form with operators, and using crucially JHC Whitehead's notion of crossed module, a term not in Hatcher's book. |
May 24 |
awarded | Good Answer |
May 22 |
comment |
What's a groupoid? What's a good example of a groupoid?
This discussion should be linked to mathoverflow.net/questions/40945/… |
May 20 |
revised |
Is there a (satisfying) proof that cellular cohomology is isomorphic to simplicial cohomology that doesn't use relative cohomlogy?
added a link |
May 19 |
awarded | Yearling |
May 14 |
answered | Is there a (satisfying) proof that cellular cohomology is isomorphic to simplicial cohomology that doesn't use relative cohomlogy? |
May 14 |
awarded | Necromancer |
May 10 |
awarded | Nice Answer |