Timeline for Example of a manifold which is not a homogeneous space of any Lie group
Current License: CC BY-SA 3.0
4 events
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| Feb 25, 2012 at 0:21 | comment | added | Vitali Kapovitch | @Igor sorry, this was not clear from your answer. the OP states the question 3 times and only mentions compactness once. He should modify the question IMO. It's also clear from this comments that he is interested in the general case and it creates confusion because some answers assume that G is compact and others do not. | |
| Feb 24, 2012 at 22:55 | comment | added | Igor Belegradek | @Vitali: I was answering to OP's request "in finding an example of a compact manifold which is not a homogeneous space of any compact Lie group". If a compact Lie group acts transitively on a manifold, then the isotropy subgroup is closed, hence compact. | |
| Feb 24, 2012 at 19:30 | comment | added | Vitali Kapovitch | the OP is interested in a more general situation than homogeneous Riemannian manifolds (see his comments above). thus one can not assume that $H$ is compact. So things like quotients by uniform lattices in semisimple Lie groups or nilmanifolds are fair game. | |
| Feb 24, 2012 at 16:50 | history | answered | Igor Belegradek | CC BY-SA 3.0 |