Timeline for A Pachner complex for triangulated manifolds
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Dec 31, 2020 at 3:03 | comment | added | Ryan Budney | It appears to be closely connected to the fundamental group of the manifolds. For example, if the 4-manifold has a finite fundamental group it could very well have a finite mapping-class group. But for manifolds like $S^1 x D^3$ the mapping class group is infinite -- I'm taking diffeomorphisms that are the identity on the boundary. It's quite the contrast with dimension 3 where all diffeomorphisms of a handlebody that are identity on the boundary are isotopic to the identity. It has more in common with what happens in high dimensions. | |
| Dec 29, 2020 at 22:14 | comment | added | Sam Nead | @RyanBudney - I did not previously know that the mapping class group of a four-manifold could be infinitely generated. How completely terrifying! I suppose that the natural guess is that the graph above (where only (3,3) moves are allowed) may have infinitely many components. What is the stabiliser of a connected component? | |
| Dec 29, 2020 at 18:31 | comment | added | Ryan Budney | Hi Sam. I think this question had its origin in some conversations with Ben Burton and Hyam Rubinstein, 10+ years ago. 3-3 moves have a pleasant finitary nature to them, so I don't see how one could get to mapping class groups being not finitely generated. | |
| Dec 26, 2020 at 15:36 | history | answered | Sam Nead | CC BY-SA 4.0 |