Timeline for Is $\mathrm{Diff}_0(S_g)$ torsion-free?
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 7, 2016 at 19:55 | answer | added | Tom Church | timeline score: 2 | |
| Sep 18, 2016 at 14:25 | vote | accept | Jens Reinhold | ||
| S Sep 18, 2016 at 4:17 | history | suggested | user50085 | CC BY-SA 3.0 |
Latexified the title
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| Sep 18, 2016 at 3:05 | review | Suggested edits | |||
| S Sep 18, 2016 at 4:17 | |||||
| Sep 18, 2016 at 2:17 | answer | added | Andy Putman | timeline score: 12 | |
| Sep 17, 2016 at 19:59 | answer | added | Danny Ruberman | timeline score: 10 | |
| Sep 17, 2016 at 15:54 | comment | added | Misha | @HJRW: I just did. | |
| Sep 17, 2016 at 15:52 | answer | added | Misha | timeline score: 11 | |
| Sep 17, 2016 at 8:06 | comment | added | HJRW | @Misha, would you consider adding your comment as an answer? | |
| Sep 17, 2016 at 2:49 | comment | added | Misha | @JensReinhold: That's right: The lifting always exists and it always extends to a homeomorphism of the closure of the Poincare disk. But since the action on $\pi_1$ is trivial, the extended action is by the identity on the boundary circle. Now you use either Smith' theory or a theorem by Newmann (?) to conclude that the periodic homeomorphism is the identity map. | |
| Sep 16, 2016 at 15:52 | comment | added | Jens Reinhold | Ahh, that's quite simple actually, thanks. The lifting works because the action on the fundamental group has to be trivial, I guess. | |
| Sep 16, 2016 at 15:07 | comment | added | Misha | Yes, this group is torsion free. The same for homeomorphisms. Hint: Lift to a periodic homeomorphism of the hyperbolic plane and extend to a homeomorphism of the sphere fixing an open disk pointwise. | |
| Sep 16, 2016 at 15:00 | comment | added | Mark Grant | @FrancescoPolizzi: The question is whether this rotation is isotopic to the identity. My feeling (and at the moment it is just a feeling) is that if you had a torsion element in $Diff_0(S_g)$ you could use it to produce a smooth effective action of a circle on $S_g$, and that such an action may not exist. | |
| Sep 16, 2016 at 14:54 | comment | added | Francesco Polizzi | What if you take a surface $S_g \subset \mathbb{R}^3$ which is symmetric with respect to the $z$-axis, and consider a rotation of $180$ degrees with respect to this axis? This should be an orientation-preserving diffeomorphism of order $2$, right? | |
| Sep 16, 2016 at 14:41 | history | asked | Jens Reinhold | CC BY-SA 3.0 |