Timeline for Does every triangulable manifold have a vertex-transitive triangulation?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 17, 2023 at 22:43 | vote | accept | Mike | ||
| May 18, 2023 at 14:21 | answer | added | Misha | timeline score: 6 | |
| May 17, 2023 at 9:16 | history | edited | YCor | CC BY-SA 4.0 |
edited the question to include it in body and add necessary condition
|
| May 16, 2023 at 20:01 | answer | added | Ian Agol | timeline score: 7 | |
| Feb 26, 2023 at 14:52 | comment | added | Mike | Most compact surfaces have flag transitive triangulations, This is connected with the theory of regular maps and Hurwitz groups (Conder, Macbeath, Singerman, Siran, Tucker and others). Here's an example of what I'm talking about: sciencedirect.com/science/article/pii/0095895685900620 | |
| Feb 26, 2023 at 13:05 | comment | added | Ben McKay | I suppose we would all guess that compact surfaces of genus 2 or more, since they have no transitive Lie group action, have no vertex-transitive triangulation, and lower genus compact surfaces probably have a vertex-transitive triangulation. | |
| Feb 26, 2023 at 2:58 | comment | added | Mike | It's a good question. Does every PL manifold have a rigid triangulation, in some sense? I don't think this is known even for 2-manifolds. | |
| Feb 26, 2023 at 0:30 | comment | added | Ryan Budney | It takes my brain a while to "warm up" to some questions, apologies. I'm getting there. | |
| Feb 25, 2023 at 23:03 | comment | added | Mike | That's an interesting question but, if I understand you correctly, it's the opposite of what I'm interested in. I'm interested in whether every PL manifold M has a vertex transitive triangulation X, so Aut(X) is large. It would be interesting if, as you suggest, some or all PL manifolds have triangulations with Aut(X) trivial. | |
| Feb 25, 2023 at 22:57 | comment | added | Ryan Budney | I would imagine the answer is no. For example, you can find semi-simplicial triangulated (delta complex) manifolds so that the automorphism group is trivial. You could then barycentrically subdivide that triangulation twice to turn it into a proper simplicial complex. I don't imagine the automorphism group becomes any larger, but I suppose there's something to check there. | |
| Feb 25, 2023 at 22:54 | comment | added | Mike | Yes, thanks. I'm not going to go into the complexities for topological manifolds. | |
| Feb 25, 2023 at 22:53 | comment | added | Ryan Budney | Presumably this question is for PL-manifolds. | |
| Feb 25, 2023 at 22:38 | comment | added | Dave Benson | Not every manifold is triangulable, so maybe you need to reformulate your question. | |
| S Feb 25, 2023 at 21:46 | review | First questions | |||
| Feb 26, 2023 at 3:16 | |||||
| S Feb 25, 2023 at 21:46 | history | asked | Mike | CC BY-SA 4.0 |