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Results tagged with lie-groups
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user 20787
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
11
votes
Example of a manifold which is not a homogeneous space of any Lie group
I would think that many examples from 3-manifold theory would work. Take any compact, oriented, irreducible 3-manifold $M$ whose torus decomposition is nontrivial and has at least one hyperbolic piece …
- 15.4k
10
votes
Diffeomorphisms of the sphere conjugate to a rotation
I doubt there can be a simple answer to the first question. Even the analogous question regarding $S^1$ has no simple answer. According to work of Denjoy, given a homeomorphism $f : S^1 \to S^1$ with …
- 15.4k
9
votes
Accepted
discrete subgroups of Lie groups and actions on homogeneous spaces
Here is a simple counter-example. Let $p : S_3 \to S_2$ be a degree 2 covering map from the closed genus 3 surface to the closed genus 2 surface, inducing an index 2 injection $p_* : \pi_1(S_3) \to \p …
- 15.4k
7
votes
How can I tell whether a manifold is homogeneous?
Is Eberlein's theorem relevant to your question? If $M$ is a compact Riemannian manifold of nonpositive section curvature, Eberlein's theorem MR0674166 characterizes when $M$ is a Riemannian symmetric …
- 15.4k
3
votes
Complexification or 'real'ization of Mapping Class group.
As Misha mentions, his paper with Leeb, "Actions of discrete groups on nonpositively curved spaces" MR1411351, gives severe restrictions on CAT(0) structures on $MCG(S)$, which covers the case of latt …
- 15.4k