Timeline for Lifting from mapping class group to groups of homeo/diffeomorphisms
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 5, 2017 at 8:53 | vote | accept | Jesús Álvarez | ||
| Feb 27, 2017 at 5:11 | history | edited | YCor | CC BY-SA 3.0 |
changed to more precise title and added tags
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| Feb 26, 2017 at 23:02 | comment | added | Ryan Budney | What you are asking is a standard symmetry question. If you think of the mapping class group in terms of diffeomorphisms, you are asking the lifting problem for subgroups of $\pi_0 Diff(M)$, under the projection map $Diff(M) \to \pi_0 Diff(M)$. Generally you need to know something about the manifold to answer questions about this problem, there's little general-nonsense to rely on. Take a look at Sakuma's work on knot exteriors in $S^3$, it's quite beautiful. There is of course plenty to work with in low dimensions. | |
| Feb 26, 2017 at 22:53 | answer | added | Nick Salter | timeline score: 6 | |
| Feb 13, 2017 at 11:55 | comment | added | Jesús Álvarez | I'm mainly interested in the differentiable setting: self-diffeomorphisms and diffeotopies, but the continuous setting would be also interesting. The question is very general because I don't know any concrete situation with some hope of an answer. | |
| Feb 13, 2017 at 2:37 | comment | added | YCor | As mentioned several times by other users, the definition of MCG is unclear in higher dimension (self-homeomorphisms or self-diffeomorphisms? what kind of isotopies?...) | |
| Feb 13, 2017 at 0:56 | comment | added | YCor | Sounds a bit general. Even the case when $G$ is the mapping class group and the homomorphism is the identity is unclear. | |
| Feb 12, 2017 at 23:29 | history | asked | Jesús Álvarez | CC BY-SA 3.0 |