Timeline for Does every triangulable manifold have a vertex-transitive triangulation?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 18, 2023 at 21:42 | history | edited | Misha | CC BY-SA 4.0 |
added 21 characters in body
|
| May 18, 2023 at 21:40 | comment | added | Misha | @IanAgol: It is theorem 9.5 in Bredon's book (that he attributes to Newman) that the interior has to be empty. Bredon also explains a reduction to Newman’s theorem on the size of the displacement. Yes, in the nutshell, the idea is to shrink the support set of a period $p$-map using conformal rescaling in the spherical case. But the theorem also works for all manifolds, not just spheres. | |
| May 18, 2023 at 20:16 | comment | added | Ian Agol | Okay, I was thinking that something along these lines ought to work. To apply Newman’s theorem, I guess you can just shrink hyperbolic space down by a conformal transformation so that the period translates as little as you like, a contradiction? I was trying to apply a theorem of Smith which says that the fixed point set of a periodic homemorphism on euclidean space has the mod p homology of a point, but I missed that there is a local version. | |
| May 18, 2023 at 14:21 | history | answered | Misha | CC BY-SA 4.0 |