Timeline for Finding an irreducible region of a space given a group of transformations
Current License: CC BY-SA 4.0
8 events
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| Aug 9, 2020 at 15:15 | comment | added | Moishe Kohan | @Mason: No, in the simplicial case one uses a different construction (via a maximal subtree in the dual graph). It is not more general than Voronoi, just different. As for guidance, it depends on how your manifold and the action is given. Maybe your manifold is given by its triangulation? In general, finding an invariant triangulation is not easy and most arguments would yield an invariant metric and a Voronoi tiling as well. | |
| Aug 7, 2020 at 23:39 | comment | added | Mason | Also, do you have any guidance on how I can tell if a given group will act simplicially? | |
| Aug 7, 2020 at 23:38 | comment | added | Mason | I've been trying to understand your link but I think I'm still confused. Are you saying that if G is finite and acts simplicially, then the Voronoi technique above is still valid? Or are you saying that your link shows a more general method different from Voronoi? | |
| Jul 31, 2020 at 22:41 | comment | added | Moishe Kohan | @Mason: Yes, but you need some assumptions on the action of $G$: $G$ is finite and acts simplicially (preserves some triangulation). See math.stackexchange.com/questions/3047013/… | |
| Jul 30, 2020 at 3:16 | comment | added | Mason | Is there a generalization of this which doesn't assume that $G$ acts isometrically? | |
| Jul 20, 2020 at 3:22 | vote | accept | Mason | ||
| Jul 20, 2020 at 3:21 | comment | added | Mason | That is a beautiful technique, thank you! If you're interested, I put a bounty on essentially the same question on Math Stack Exchange: math.stackexchange.com/questions/1284436/…. If you also submit your answer there, you should be able to claim the bounty. | |
| Jul 18, 2020 at 20:57 | history | answered | Moishe Kohan | CC BY-SA 4.0 |