Timeline for Analogues of the curve complex for Out(F)
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Sep 24, 2013 at 12:08 | vote | accept | HJRW | ||
| Sep 22, 2013 at 14:57 | answer | added | Lee Mosher | timeline score: 7 | |
| Sep 22, 2013 at 6:36 | comment | added | HJRW | @LeeMosher - I was referring to the fact that the curve complex is flag and so can be reconstructed easily from the curve graph. I wanted to explain the fact that some of the free-group analogues are just graphs. Next time I edit the question, I'll try to make this clearer. | |
| Sep 22, 2013 at 3:29 | comment | added | Lee Mosher | It's misleading to say that "all the information" about the curve complex is contained in its one-skeleton. As shown by Harer, the homotopy type of the curve complex is a wedge of spheres, and this is used in establishing the v.c.d. of the mapping class group. | |
| Sep 20, 2013 at 16:20 | comment | added | Andy Putman | @staylor : That space is useful in other contexts too. For instance, Matt Day and I used a version of it to study the Torelli subgroup of $\text{Aut}(F_n)$ in our paper The complex of partial bases for $F_n$ and finite generation of the Torelli subgroup of $\text{Aut}(F_n)$ and gave descriptions of the stabilizers of simplices in it in our paper A Birman exact sequence for $\text{Aut}(F_n)$. | |
| Sep 20, 2013 at 14:48 | comment | added | HJRW | @staylor, Yes! The list is not meant to be exhaustive - just to indicate the scale of the problem for a non-expert interested in the area. An account of which complexes are known to be quasi-isometric to each other is exactly the sort of information that I'd be interested in. | |
| Sep 20, 2013 at 14:40 | comment | added | staylor | Can I add to the list? The graph whose vertices are conjugacy classes of rank 1 factors and whose edges correspond to pairs of vertices represented by elements that generate a rank 2 factor is quasi-isometric to the factor complex (as are others in your list) but has local properties similar to the curve complex. For example, this graph interacts nicely with subfactor projections. | |
| Sep 20, 2013 at 12:42 | history | edited | HJRW | CC BY-SA 3.0 |
Improved the readibility of the main question.
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| Sep 20, 2013 at 11:39 | history | asked | HJRW | CC BY-SA 3.0 |