Timeline for When does the sheaf cohomology of a topological space vanish?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Feb 11, 2014 at 0:26 | history | edited | Ricardo Andrade |
replaced deprecated tag 'topology'; added relevant tags
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| Apr 14, 2013 at 0:27 | comment | added | Tom Goodwillie | (The Cantor set is homeomorphic to $\mathbb Z_p$.) | |
| Apr 13, 2013 at 23:38 | comment | added | anon | Thanks! If you write this as an answer, I would be happy to accept it. | |
| Apr 13, 2013 at 21:47 | comment | added | user31960 | A compact Hausdorff space has the property you want if and only if it is totally disconnected. See theorem II.16.21 Bredon, "Sheaf theory" (second edition, GTM 170). Examples of compact totally disconnected spaces are the Cantor set and $\mathbb{Z}_p$. | |
| Apr 13, 2013 at 19:56 | comment | added | Tom Goodwillie | If every open cover of $X$ has a refinement consisting of disjoint open sets, then every (locally) surjective map of sheaves on $X$ is surjective on global sections, so that higher sheaf cohomology is trivial. | |
| Apr 13, 2013 at 17:59 | comment | added | André Henriques | Before the Cantor set, you might want to look at the one point compactification of $\mathbb N$. | |
| Apr 13, 2013 at 17:34 | history | edited | anon | CC BY-SA 3.0 |
Added clarification about the pathological nature of these spaces.
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| Apr 13, 2013 at 12:37 | answer | added | Georges Elencwajg | timeline score: 10 | |
| Apr 13, 2013 at 5:28 | history | asked | anon | CC BY-SA 3.0 |