Timeline for Dimension of a set detected by a homology class
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 18, 2014 at 16:25 | vote | accept | Tom Goodwillie | ||
| Apr 18, 2014 at 13:38 | answer | added | Anton Petrunin | timeline score: 5 | |
| Apr 18, 2014 at 12:23 | comment | added | Tom Goodwillie | Certainly some kind of $p$th Cech cohomology of $C$ is nontrivial. My question is, what does this imply geometrically about $C$? | |
| Apr 18, 2014 at 4:26 | comment | added | Włodzimierz Holsztyński | First there was the absolute (just for the spaces, not for subsets) Poincare duality theorem. Then there was Alexander-Pontryagin theorem for subsets of a manifold. On the later occasion Pontryagin introduced his duality theorem for topological groups--initially it was about compact abelian groups versus discrete abelian groups. (This was generalized to locallyt compact abelian groups Egbert van Kampen in 1935 and André Weil in 1940--see wikipedia). An early result about dissecting $\mathbb R^n$ by a compact subset was obtained by Karol Borsuk. Etc. (you need to ask not me but a specialist). | |
| Apr 18, 2014 at 1:48 | comment | added | Tom Goodwillie | What are the topological duality theorems? | |
| Apr 18, 2014 at 0:55 | comment | added | Włodzimierz Holsztyński | That's what the topological duality theorems are about. | |
| Apr 17, 2014 at 23:38 | history | asked | Tom Goodwillie | CC BY-SA 3.0 |