Timeline for Poincare conjecture and the graph of triangulations
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Nov 25, 2010 at 17:19 | comment | added | Sam Nead | @Ryan - Correct. The point I was making is that the Mijatovic/King algorithm is very simple (brute force search) but slow. @Mark - That is what I am saying. You give me a triangulated manifold, say with $n$ tetrahedra. I produce all triangulations within distance $e^{e^n}$ in the triangulation graph. Then using Mijatovic/King one of those triangulations is the boundary of a four simplex iff the manifold you gave me was $S^3$. | |
| Nov 24, 2010 at 15:06 | comment | added | user6976 | @Ryan and @Sam: I thought that Sergei Ivanov (from Illinois) proved that recognizing sphere is in NP. Anyway, the problem which I am looking for is about the (a) graph of triangulations and the length (existence) of a path between two triangulations on that graph. | |
| Nov 23, 2010 at 21:57 | comment | added | Ryan Budney | The double-exponential algorithm you refer to is presumably for finding a sequence of Pachner moves to a standard triangulation. 3-sphere recognition (no Pachner moves, just Rubinstein's alg) is single-exponential run-time. | |
| Nov 23, 2010 at 21:51 | history | answered | Sam Nead | CC BY-SA 2.5 |