Timeline for generalisations of the Seifert-van Kampen Theorem?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 16, 2012 at 22:04 | answer | added | Mike Shulman | timeline score: 16 | |
| Jul 16, 2012 at 19:44 | history | edited | Mike Shulman |
added some tags
|
|
| Jul 16, 2012 at 11:05 | comment | added | Ronnie Brown | That is a reasonable suggestion, and concurs with +1 to deal with homotopies (for the strict structures of our fundamental higher groupoids), and another +1 to deal with the covering dimension. Of course Higgins and I have good reasons for using cubical rather than simplicial methods. Major features of the two strands of work are (i) that they deal with structured spaces (filtered or $n$-cubes), and (ii) that the construction of the corresponding "fundamental" object, essential to the work, is not straightforward. | |
| Jul 15, 2012 at 22:28 | answer | added | Akhil Mathew | timeline score: 4 | |
| Jul 15, 2012 at 21:17 | comment | added | Mike Shulman | My guess would be that 3 is 1+2, where 1 is the dimension of the groupoids in question (the classical SvKT is about 1-groupoids) and 2 is a universal constant for $n$-colimits --- a colimit of $n$-groupoids can be calculated using coproducts and realizations of truncated simplicial objects (generalized coequalizers) with $n+2$ terms. If we were calculating the fundamental 0-groupoid $\pi_0$, we should only need 1- and 2-fold intersections, and similarly for fundamental $n$-groupoids we should expect to need up to $(n+2)$-fold intersections. | |
| Jul 15, 2012 at 16:52 | history | asked | Ronnie Brown | CC BY-SA 3.0 |