Timeline for Can one glue De Rham cohomology classes on a differential manifolds?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| May 13, 2022 at 16:55 | comment | added | Georges Elencwajg | @Mark Grant: Indeed the Mayer-Vietoris theorem says exactly that for a covering with two open pieces, glueing is always possible. So Will's nice counter-example is the most economical possible. | |
| May 13, 2022 at 16:51 | comment | added | Georges Elencwajg | Thank you, dear Will: this is, as always with you, an excellent answer. | |
| May 13, 2022 at 16:11 | vote | accept | Georges Elencwajg | ||
| May 12, 2022 at 15:11 | comment | added | Will Sawin | @MarkGrant The statement is trivially true if all open sets are contractible, as then the cohomology groups vanish so any closed global differential form does the trick, which is a bit weaker than being a good cover. | |
| May 12, 2022 at 14:58 | comment | added | Mark Grant | I think it should also be true for good covers, by applying what Bott & Tu call the "Mayer-Vietoris principle" in Section 8 of their book Differential Forms in Algebraic Topology. | |
| May 12, 2022 at 11:57 | history | answered | Will Sawin | CC BY-SA 4.0 |