Timeline for Compelling evidence that two basepoints are better than one
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 26, 2014 at 16:15 | comment | added | Ronnie Brown | @HJRW: In mathematics, I feel there can often be a world of difference between "implicit" and "explicit", especially if the latter is followed by exploitation. See for example this paper PAUL LUNAU, Int. J. Algebra Comput., 15, 129 (2005). For me, the chief advantage of groupoids was that they led to higher homotopy groupoids, see presentations in 2014 at Paris, IHP, and Galway, on my preprint page. | |
| Apr 22, 2013 at 14:33 | comment | added | HJRW | Ronnie, this last comment begs the question. The reason Higgins' paper 'has been ignored by the specialists' is that it isn't particularly useful: the groupoid normal form isn't importantly different from the usual group normal form. (Also, the groupoid normal form is already implicit in Serre's work.) | |
| Jan 25, 2012 at 7:44 | comment | added | Ronnie Brown | Following up the last comment, see the paper Higgins, P.J. The fundamental groupoid of a graph of groups. J. London Math. Soc. (2) 13~(1) (1976) 145--149. which gives a normal form without any choice of base point or tree, and has been ignored by the specialists. One can regard the method as "distributed computing", with one computer at each vertex, analysing a word as it passes through. Emma Moore at Bangor did a nice thesis on this (2001). | |
| Oct 3, 2010 at 20:17 | comment | added | André Henriques | A graph of groups is to a graph what an orbifold is to a manifold. So a graph of groups is very much related to groupoids, just like orbifolds are. | |
| Oct 3, 2010 at 19:31 | comment | added | Ryan Budney | Isn't this just a re-labelling of an older technique that combinatorial and geometric group theorists call a "graph of groups" argument/construction or Bass-Serre theory? | |
| Oct 3, 2010 at 19:22 | history | answered | Robert Bell | CC BY-SA 2.5 |