Timeline for Diff(M) and connectedness
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 19, 2013 at 0:37 | vote | accept | Koushik | ||
| Feb 18, 2013 at 20:16 | history | edited | Andy Putman | CC BY-SA 3.0 |
added 41 characters in body
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| Feb 18, 2013 at 20:15 | comment | added | Andy Putman | @Peter Michor : Good point, I was assuming implicitly that everything was compact anyway. I'll add that assumption to the answer. | |
| Feb 18, 2013 at 20:14 | comment | added | Andy Putman | @Will Sawin : I don't think this is a problem since I restricted myself to the connected component of the identity in $\text{Diff}(M)$; such elements cannot permute the components around (which is the problem I think you were referring to). I spent a little time before writing this trying to come up with a clean formulation of what happens to $\text{Diff}(M)$ when some components are diffeomorphic. I couldn't find one, so I took the easy way out. | |
| Feb 18, 2013 at 18:11 | comment | added | Peter Michor | Part 1, only if all connected components of $M$ are compact, or if you consider the connected component of the group of diffeomorphisms with compact support. | |
| Feb 18, 2013 at 18:03 | comment | added | Will Sawin | For part 2, only if $M$ and $N$ are not diffeomorphic. | |
| Feb 18, 2013 at 17:52 | history | answered | Andy Putman | CC BY-SA 3.0 |