Timeline for Has dynamics on $G/\Gamma$ ever been used to prove interesting things about $\Gamma$?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 21, 2018 at 16:48 | comment | added | Ian Agol | Yes, there’s a lot more that goes into it than just exponential mixing. I guess though that this remains an essential part in this sort of surface subgroup theorem. | |
| Sep 21, 2018 at 15:40 | comment | added | HJRW | @Kim, Ian is being modest. Using tools developed by Wise and others, Ian used the work of Kahn—Markovic to deduce that hyperbolic 3-manifold groups are virtually special, which in turn resolved many famous open problems. Sample applications: virtual Haken, virtual fibring, LERF, largeness... All of these can be phrased as group-theoretic properties of $\Gamma$. | |
| Sep 21, 2018 at 15:06 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Sep 21, 2018 at 14:02 | comment | added | Ian Agol | @Kim : this has been generalized by many people to other lattices. Gromov conjectured hyperbolic groups have a surface subgroup. For other consequences, see my survey for the ICM proceedings (you can find it on my homepage). | |
| Sep 21, 2018 at 5:41 | comment | added | Kim | Could you elaborate? What kind of interesting things do we learn about $\Gamma$ when we know it contains a surface subgroup? | |
| Sep 21, 2018 at 4:59 | history | answered | Ian Agol | CC BY-SA 4.0 |