Timeline for Cubical Complexes and Bass-Serre theory
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 13, 2012 at 13:24 | vote | accept | ADL | ||
| Dec 12, 2012 at 17:38 | comment | added | HJRW | (cont'd)... The example to bear in mind is an immersed, non-embedded, curve $gamma$ on a surface $\Sigma$. It generates a codimension-one subgroup $\langle\gamma\rangle$ (in the sense that $\langle\gamma\rangle$ coarsely separates $\pi_1\Sigma$), but you can't cut along it, so you can't realize it as the stabilizer of an edge in an action on a tree. But you can realize is as the stabilizer of a hyperplane in an action on a square complex. | |
| Dec 12, 2012 at 17:37 | comment | added | HJRW | Not lost, but strengthened! 'Free' is much stronger than 'essential'. If you only assume that the action is 'essential' then the theory does indeed generalize Bass--Serre theory. | |
| Dec 12, 2012 at 17:03 | comment | added | ADL | Hmm - I really didn't pick up on this! (But it certainly makes sense - thanks.) Sageev talks about "essential" actions (which corresponds to not messing up the hyperplanes, and in the finite dimensional case this corresponds to an action with an unbounded orbit) - was this dropped somewhere along the way? | |
| Dec 12, 2012 at 15:16 | history | answered | HJRW | CC BY-SA 3.0 |