Timeline for Homology of compact symmetric spaces
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 13, 2014 at 15:48 | comment | added | user2529 | Could I ask what application do you have this homology information for? | |
| Feb 9, 2014 at 7:00 | comment | added | user43326 | Probably <a href="mathoverflow.net/questions/78717/… question </a> is relevant. Anyhow there is a book by Toda and Mimura (in Japanese, unfortunately) with a table of cohomology of classical homogeneous spaces. | |
| Feb 9, 2014 at 3:54 | comment | added | JHM | Your question asks for $G/U$ where you've declared $U$ to be the fixed point set of an involution on $G$. This is much more general than Cartan's symmetric spaces. E.g. implies nothing about the quotient being locally homogeneous nor the involution being an isometry for the Killing form. | |
| Feb 9, 2014 at 3:32 | comment | added | Marty | Have you checked in a book like Joe Wolf's "Spaces of Constant Curvature" | |
| Feb 9, 2014 at 2:37 | comment | added | Edgardo | Yes, the symmetric spaces were classified by E. Cartan. See en.wikipedia.org/wiki/Symmetric_space#Classification_result for the list. However, I haven't seen anywhere a list of their homologies. Probably it was done in the 1950s, but I couldn't find it in e.g. the Borel-Hirzebruch papers. | |
| Feb 9, 2014 at 1:41 | comment | added | JHM | what makes you think that this list can even be finitely generated? e.g. are you aware there being only finitely many involutions (modulo conjugation) for the sequence of groups $SO(n), n=1,2,3, \ldots$ ? | |
| Feb 8, 2014 at 18:41 | history | asked | Edgardo | CC BY-SA 3.0 |