Timeline for Diffeomorphisms of a surface in terms of generators.
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 2, 2012 at 15:52 | comment | added | Igor Rivin | @Lee actually, there are two natural ways: one: the homeo is given as a simplicial map. In the other we are given an automorphosm of the fundamental group. | |
| Jul 2, 2012 at 15:32 | comment | added | Lee Mosher | From Andrew's comment to Igor's question below, it looks to me like the question should be something like this: given a particular element of the mapping class group, say the mapping class of a homeomorphism or diffeomorphism expressed in some concrete manner, is there a procedure which will produce a word in the standard generators of the mapping class group which represents the given mapping class? This is still not a very good question because it does not specify concretely how the mapping class is given. | |
| Jul 2, 2012 at 2:15 | comment | added | user5810 | "a presentation of a diffeomorphisms" ? $\:$ | |
| Jul 2, 2012 at 0:00 | answer | added | Igor Rivin | timeline score: 4 | |
| Jul 2, 2012 at 0:00 | comment | added | MTS | This is still not clear. Are you asking for an example of a surface with explicit generators and relations for the group of diffeomorphisms of the surface? Or, as your comment seems to indicate, are you asking for an example of a surface $S$ with presentations of the higher homotopy groups $\pi_n(S)$? Diffeomorphisms up to homotopy (i.e. the mapping class group)? There are too many possible interpretations for this question. You are more likely to get a good response if you make it clear exactly what you are after. | |
| Jul 1, 2012 at 23:30 | comment | added | Andrew | Of course I mean generators of homeotopy group. | |
| Jul 1, 2012 at 22:25 | comment | added | MTS | Your question is not clear to me. Do you mean a presentation of the group of diffeomorphisms? Or something else? | |
| Jul 1, 2012 at 22:19 | history | asked | Andrew | CC BY-SA 3.0 |