Timeline for Combinatorial results by Poincaré duality
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Jun 18, 2015 at 16:13 | comment | added | Timothy Chow | Stanley's survey paper on unimodal sequences is a possible starting point. dedekind.mit.edu/~rstan/pubs/pubfiles/72.pdf However, I don't think that it gives any examples other than the ones already mentioned. In general, I think it would be very unusual for the symmetry of a sequence to be provable most easily by a topological duality theorem, rather than by a direct combinatorial argument. Even the Dehn--Sommerville equations have a relatively straightforward combinatorial proof. | |
| Jun 18, 2015 at 14:49 | comment | added | Rolf Bardeli | I am willing to extend to any other duality concepts in (co-)homology. | |
| Jun 18, 2015 at 14:41 | history | edited | Rolf Bardeli | CC BY-SA 3.0 |
added 146 characters in body
|
| Jun 18, 2015 at 14:32 | comment | added | Allen Knutson | If you're willing to extend this from "Poincar\'e duality" to "properties of Betti numbers", then you could include Hard Lefschetz in your toolset, and get Stanley's proof of the Upper Bound Theorem for the number of faces of a simplicial polytope. | |
| Jun 18, 2015 at 14:20 | comment | added | Dylan Wilson | Someone who knows about toric varieties surely has something to say here... (Poincaré duality holds for these with rational coefficients) | |
| Jun 18, 2015 at 11:06 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Jun 18, 2015 at 7:46 | review | First posts | |||
| Jun 18, 2015 at 7:50 | |||||
| Jun 18, 2015 at 7:43 | history | asked | Rolf Bardeli | CC BY-SA 3.0 |