Timeline for connectivity of the group of orientation-preserving homeomorphisms of the sphere
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
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| Nov 29, 2010 at 6:38 | vote | accept | Keivan Karai | ||
| Sep 25, 2010 at 20:34 | history | edited | Sean Tilson |
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| Sep 25, 2010 at 17:35 | comment | added | Dmitri Panov | Couple of days ago there was a nice paper in arxiv on a related topic: Decomposing diffeomorphisms of the sphere arxiv.org/abs/1009.3905 | |
| Sep 25, 2010 at 17:25 | history | edited | BS. |
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| Sep 25, 2010 at 17:17 | answer | added | BS. | timeline score: 32 | |
| Sep 20, 2010 at 19:19 | comment | added | Tom Goodwillie | In many cases the diffeomorphism group is "bigger". For example, the space of self-homeomorphisms of the closed $n$ disk fixing the boundary pointwise is contractible, while for large values of $n$ the analogous space of diffeomorphisms has plenty of nontrivial rational homotopy, detected by algebraic $K$-theory. | |
| Sep 20, 2010 at 19:14 | comment | added | Maxime Bourrigan | Aren't there general theorems implying that Homeo+(S^n) is a simple group? As the connected component of the identity is a normal subgroup, it would answer the question. | |
| Sep 20, 2010 at 17:36 | comment | added | Dick Palais | More generally, what is known about when the group of (orientation preserving) homeomorphisms of an (oriented) smooth manifold deformation retracts onto the group of (orientation preserving) diffeomorphisms. | |
| Sep 20, 2010 at 17:22 | comment | added | user47274 | Maybe you will find this useful (for $n=3$): ams.org/journals/proc/1960-011-02/S0002-9939-1960-0112128-9/… | |
| Sep 20, 2010 at 16:59 | history | asked | Keivan Karai | CC BY-SA 2.5 |