Timeline for Euler Characteristic of $SL_m(\mathbb{C})/SO_m(\mathbb{C})$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Sep 23, 2019 at 9:21 | vote | accept | Winnie_XP | ||
| Sep 23, 2019 at 0:26 | comment | added | Winnie_XP | Thanks @Venkataramana, that's very helpful, I will look them up in details. | |
| Sep 22, 2019 at 0:07 | history | edited | Sean Lawton | CC BY-SA 4.0 |
minor edit
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| Sep 21, 2019 at 22:59 | answer | added | Sean Lawton | timeline score: 6 | |
| Sep 20, 2019 at 7:25 | review | Close votes | |||
| Sep 20, 2019 at 18:03 | |||||
| Sep 20, 2019 at 6:51 | comment | added | Venkataramana | This is something very classical. You can replace the groups by their maximal compacts up to homotopy. Hence the space is homotopic to the quotient $SU(n)/SO(n)$. The Euler characteristic is zero unless $n=2$. For compact connected groups $H\subset G$, the Euler characteristic is zero unless both $G,H$ have the same rank, in which case, it is strictly positive. You may see A.Borel's early papers. | |
| Sep 20, 2019 at 5:38 | history | asked | Winnie_XP | CC BY-SA 4.0 |