Timeline for finiteness of the dimensions of cohomologies of open subsets of a compact manifold
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Jun 13, 2012 at 17:08 | comment | added | Alberto Jermaine | I think I can construct a counterexample now. Let $M$ be a circle $\mathbb R/\mathbb Z$, $U=M$ and $V=M−\{1/2^i+\mathbb Z:i\in\mathbb N\}$. Then at least $H^0(V)$ is infinite dimensional. | |
| Jun 13, 2012 at 16:51 | comment | added | Igor Rivin | I was going to give @Angelo's example, but since he beat me to it, I should just note that this can be done in any dimension up to $n-1$ | |
| Jun 13, 2012 at 16:48 | comment | added | Angelo | Choose as one of the two subsets the disjoint union of infinitely many non-empty open subsets; in this case the $H^0$ is not finitely dimensional. | |
| Jun 13, 2012 at 16:43 | history | asked | Alberto Jermaine | CC BY-SA 3.0 |