Timeline for Free $S^1$-action on compact homogeneous spaces
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 9, 2022 at 0:47 | vote | accept | abracadabra12345 | ||
| Nov 8, 2022 at 17:23 | answer | added | mme | timeline score: 2 | |
| Nov 8, 2022 at 16:57 | history | edited | abracadabra12345 | CC BY-SA 4.0 |
added 49 characters in body
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| Nov 8, 2022 at 16:57 | comment | added | abracadabra12345 | Thanks for your answer! Yes, I was considering $K$ connected, but nevertheless what you gave is great. I'll update the question | |
| Nov 8, 2022 at 14:22 | comment | added | mme | If this were true then the manifold would be a principle circle bundle over the quotient. If $G/K$ is a 3-manifold with $b_1 = 0$, this implies $G/K$ is diffeomorphic to a lens space $L(n,1)$. Thus a great many spherical 3-manifolds give counterexamples, such as the Poincare homology sphere where $G = SO_3$ and $K = A_5$ is the discrete group of symmetries of the icosahedron. Maybe you have better luck with K connected? | |
| Nov 8, 2022 at 4:26 | history | asked | abracadabra12345 | CC BY-SA 4.0 |