Timeline for discrete subgroups of Lie groups and actions on homogeneous spaces
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 4, 2013 at 8:43 | vote | accept | Dieter | ||
| Mar 4, 2013 at 8:43 | |||||
| Mar 4, 2013 at 8:41 | comment | added | Dieter | Thanks, this is a very nice answer. Together with Lee Mosher's answer it provides a full answer to my question, i.e. both positive and negative examples. I would like to accept them both, but since this is impossible I will accept Lee Mosher's answer because it was first. | |
| Mar 2, 2013 at 22:51 | history | edited | Misha | CC BY-SA 3.0 |
added 823 characters in body
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| Mar 2, 2013 at 21:39 | history | edited | Misha | CC BY-SA 3.0 |
added 497 characters in body
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| Mar 2, 2013 at 21:25 | comment | added | Igor Belegradek | Oh, the reference is to "Hyperbolic groups with low-dimensional boundary" not to "Geometry of quasi-planes"; sorry I got confused | |
| Mar 2, 2013 at 21:13 | comment | added | Misha | Igor, pages in pdf file for some reason do not show up, but it is p. 37-38, after Lemma 3.9. The link is correct. If you prefer archive version arxiv.org/pdf/math/9911003.pdf, it is on pages 41-43. Concerning your 1st question: The result is indeed stated for coarse PD(3) spaces, which does not include contractible 3-manifolds which are not uniformly acyclic. However, if you go through the proof(s), you realize that the proof takes place in a certain metric neighborhood of the group orbit, so the uniform acyclicity assumption can be weakened. | |
| Mar 2, 2013 at 20:36 | comment | added | Igor Belegradek | In fact, the reference points to "Geometry of quasi-planes". Could you give a page reference? | |
| Mar 2, 2013 at 20:18 | comment | added | Igor Belegradek | Misha, where do you prove that "$\tilde\Gamma$ cannot act properly discontinuously on any contractible 3-manifold"? I only found a proof that $\tilde\Gamma$ cannot act on a coarse PD(3) space (such as the universal cover of a compact aspherical 3-manifold). Of course, for your application you just need to show that $\tilde\Gamma$ cannot act properly discontinuously on the hyperbolic $3$-space, so for the example at hand everything works. | |
| Mar 2, 2013 at 17:33 | history | answered | Misha | CC BY-SA 3.0 |