Timeline for Compelling evidence that two basepoints are better than one
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Feb 16, 2022 at 4:39 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
fixed arxiv front-end link and gave title, links to appropriate pages on Peter May's website
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| Dec 17, 2020 at 10:32 | comment | added | Ronnie Brown | @HJRW Do you have an exposition of orbit spaces of a group action analogous to Chapter 11 of my book T&G? Another point is that the groupoid approach leads naturally to higher homotopy groupoids and higher Van Kampen Theorems. | |
| Jun 5, 2017 at 14:53 | comment | added | Ronnie Brown | I refer also to a comment of Gian-Carl Rota quoted at groupoids.org.uk/rota.html . Anyway, some of us have had a lot of fun from pursuing these notions over the last 50 years, and communicating them to others. | |
| Jul 22, 2014 at 14:03 | comment | added | Ronnie Brown | @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. | |
| Oct 1, 2013 at 17:41 | comment | added | Ronnie Brown | I would also like to add that the realisation that all of $1$-dimensional homotopy theory seemed to me better expressed in terms of groupoids rather than groups led me to look for the potential use of higher groupoids, from a cubical viewpoint, in higher homotopy theory; Chris Spencer, Philip Higgins and Jean-Louis Loday helped hugely to develop this idea, and its applications to new calculations in homotopy theory. | |
| Apr 22, 2013 at 10:38 | comment | added | Ronnie Brown | See also the course at Harvard on "Groupoids in topology" math.harvard.edu/~oantolin/groupoids/index.html I believe that students have less "bagage" than older workers and so can often easily catch on to the "right" concept. I first heard about groupoids in a course on homotopy theory by Michael Barratt in 1955-56. (But did not take it up till 1965.) | |
| Apr 22, 2013 at 1:05 | comment | added | Daniel Moskovich | Thank you for this answer! This past week, I just finished teaching a course out of "A concise course", following which I am convinced that indeed "the fundamental groupoid is such a natural thing, and so elementary, that it seems a little perverse to try to avoid it!", to the point that I used groupoids arguments to a greater degree that the "concise course" does in some parts of chapter 3, for example. | |
| Apr 21, 2013 at 21:18 | comment | added | Ronnie Brown | Following on from Peter's comment, it should be pointed out that the book on Nonabelian algebraic topology deals with the case of chain complexes with a groupoid of operators, and this is useful, even necessary, in relating the fundamental crossed complex $\Pi X_*$ of a CW-complex with its skeletal filtration to the cellular chains of the universal covers at various base points, see Section 8.4. Also equivariant crossed complexes are discussed in papers [94 (1997), 114 (2001)] on my web site, joint with Golasinski, Porter, and Tonks. | |
| Apr 21, 2013 at 18:52 | history | answered | Peter May | CC BY-SA 3.0 |