Timeline for A Pachner complex for triangulated manifolds
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Dec 26, 2020 at 15:36 | answer | added | Sam Nead | timeline score: 2 | |
| Aug 28, 2012 at 2:36 | comment | added | Ryan Budney | @Gil: yes, I'm discovering that paths can be terribly large. For example, there are triangulated homotopy 4-spheres with only 8 four-dimensional simplices in them, yet it takes no less than 80 Pachner 3-3 moves to go from one to the other! And this isn't rare. | |
| Aug 10, 2010 at 16:32 | comment | added | Ryan Budney | One could make it into a cubical complex by only considering collections of commuting Pachner moves but I doubt this will have many rewarding properties. I suspect Walker's suggestion, below is more or less on the right track. | |
| Aug 10, 2010 at 16:17 | answer | added | Kevin Walker | timeline score: 15 | |
| Aug 10, 2010 at 15:05 | comment | added | Gil Kalai | Very nice problem. I think the length of the Pachner path can be terribly lerribly large since deciding PL-equivalence in high dimensions is not decidable (to the best of my memory). Do you have a suggestion for the 2-cells? (not just squares, but I am not sure if we should regard every commuting moves as 2-cells.) | |
| Aug 10, 2010 at 14:31 | answer | added | Jim Fowler | timeline score: 8 | |
| Aug 9, 2010 at 23:32 | history | asked | Ryan Budney | CC BY-SA 2.5 |