Timeline for Cohomology group of a submanifold or Lie subgroup
Current License: CC BY-SA 4.0
9 events
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| Jul 13, 2021 at 14:40 | comment | added | Max Reinhold Jahnke | One possibility would be to relate the cohomology of $G$ with the cohomology of $F$ by means of the Leray spectral sequence associated with the quotient map $\pi : G \mapsto G/F$. | |
| Jun 4, 2021 at 9:08 | history | edited | Mikhail Borovoi |
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| Jun 3, 2021 at 12:37 | comment | added | Thomas Rot | There are of course relations, given by Mayer-Vietoris etc. But these answers will need a lot more imput of what $X$ is: Whitney's theorem says that any manifold is a submanifold of $\mathbb{R}^n$. The characteristic classes of the tangent/normal bundle of $X$ also have strong relations with characteristic classes of $M$. | |
| Jun 3, 2021 at 12:23 | comment | added | cherzieandkressy | Thanks! That makes the second part of my question quite trivial :) | |
| Jun 3, 2021 at 12:22 | history | edited | cherzieandkressy | CC BY-SA 4.0 |
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| Jun 3, 2021 at 11:01 | comment | added | mme | (Slight correction to Ben McKay's comment: this is true of simply connected Lie groups.) Also, a group is not empty. You mean to say $H^2(G) = 0$. | |
| Jun 3, 2021 at 10:27 | comment | added | Ben McKay | The second cohomology of any LIe group is trivial. | |
| Jun 3, 2021 at 9:58 | review | First posts | |||
| Jun 3, 2021 at 10:03 | |||||
| Jun 3, 2021 at 9:51 | history | asked | cherzieandkressy | CC BY-SA 4.0 |