Timeline for Third de Rham cohomology group for the simply connected 4-manifolds
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 3, 2017 at 17:35 | vote | accept | Ivica Smolić | ||
| Sep 2, 2017 at 19:41 | comment | added | Ivica Smolić | @abx: Yes, true... I was just hoping to find some additional assumption on the manifold that would force $H^3$ and $H^3_c$ to be isomorphic, or at least simultaneously trivial. | |
| Sep 2, 2017 at 19:36 | comment | added | abx | @Ivica: yes, the two spaces are canonically isomorphic -- this is the duality theorem (Hatcher 3.35) that you quote in your post. | |
| Sep 2, 2017 at 19:30 | comment | added | Ivica Smolić | @ David Speyer: Thanks for the very simple counterexample! But, if $H_1(\mathbb{R}^4 - \{0\}) \cong 0$, does this imply that at least $H^3_c(\mathbb{R}^4 - \{0\}) \cong 0$? | |
| Sep 2, 2017 at 19:18 | history | answered | David E Speyer | CC BY-SA 3.0 |