Timeline for De Rham cohomology of homogeneous spaces
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| May 12, 2021 at 13:43 | answer | added | Vladimir47 | timeline score: 2 | |
| Jul 31, 2019 at 11:43 | comment | added | Igor Belegradek | I got the reference from Nomizu's paper "On the Cohomology of Compact Homogeneous Spaces of Nilpotent Lie Groups" who stidies the same problem for nilmanifolds. There on page 1 Nomizu says: "For the homogeneous spaces of compact Lie groups we have the well known theory of invariant integrals of E. Cartan, namely, the cohomology of a homogeneous space of a compact Lie group can be obtained from the complex of invariant differential forms on it" with reference to theorem 2.3. | |
| Jul 31, 2019 at 11:00 | comment | added | Fofi Konstantopoulou | Thanks for the reference. I checked the paper, but it seems Theorem 2.3 deals with Lie groups, not homogeneous spaces. Also, in this case it gives a correspondence between cohomology classes and equivariant forms. Is it it clear that such forms are in correspondence with $L$-invariant elements of $\Lambda^*$ in the homogeneous space. | |
| Jul 31, 2019 at 2:20 | comment | added | Igor Belegradek | You can find a proof in Theorem 2.3 of [Chevalley-Eilenberg, Cohomology Theory of Lie Groups and Lie Algebras, Trans. Amer. Math. Soc. 63 (1948), 85–124]. The fulltext is available via google from where I am. | |
| Jul 30, 2019 at 22:31 | history | asked | Fofi Konstantopoulou | CC BY-SA 4.0 |