Timeline for Asymptotics for the number of triangulations of a manifold M
Current License: CC BY-SA 3.0
9 events
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| Aug 22, 2013 at 15:19 | history | edited | Jonah Sinick | CC BY-SA 3.0 |
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| Feb 21, 2012 at 3:02 | comment | added | Igor Rivin | @Richard: does this mean triangulations which are manifolds, or DISTINCT (topologically) manifolds? | |
| Feb 21, 2012 at 0:39 | history | edited | Jonah Sinick | CC BY-SA 3.0 |
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| Feb 21, 2012 at 0:34 | comment | added | Richard Stanley | A related result is due to Gil Kalai. He showed that the number of triangulated manifolds (of any dimension) with $n$ labelled vertices is $2^{2^{.69424\cdots n(1+o(1))}}$. See springerlink.com/content/78044667x381777g. | |
| Feb 21, 2012 at 0:27 | comment | added | Joseph O'Rourke | Following up on Ryan's pointer, Burton's paper "The Pachner graph and the simplification of 3-sphere triangulations" (arxiv.org/abs/1011.4169) includes an algorithm for "isomorph-free generation of all 3-manifold triangulations of a given size." | |
| Feb 20, 2012 at 23:52 | comment | added | Ryan Budney | Ben Burton works on this problem. I think he's pretty convinced that even for spheres, the growth-rate is super-exponential. He certainly has numerical evidence but I suspect he might eventually have a proof. | |
| Feb 20, 2012 at 23:11 | history | edited | Jonah Sinick | CC BY-SA 3.0 |
added Kontsevich reference
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| Feb 20, 2012 at 23:09 | comment | added | j.c. | See mathoverflow.net/questions/87393/… and ldtopology.wordpress.com/2012/02/05/2306 for some recent discussion | |
| Feb 20, 2012 at 22:37 | history | asked | Jonah Sinick | CC BY-SA 3.0 |