Timeline for Exotic actions of hyperbolic groups
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 7, 2015 at 16:36 | comment | added | HJRW | that seems plausible. Of course, your question would then be equivalent to a famous open problem. | |
| Jan 7, 2015 at 14:34 | comment | added | Pablo | @HJRW Yes. See arxiv.org/pdf/1308.3192v1.pdf and references therein. In fact, I suspect that I can construct such an action for EVERY hyperbolic group without finite normal subgroups (this is clearly a necessary condition). It seems that it is even possible to add the condition that every element has a fixed point. | |
| Jan 7, 2015 at 14:25 | comment | added | HJRW | Could you give an example of such an action when $G$ is free? | |
| Jan 7, 2015 at 13:45 | comment | added | Pablo | @HJRW Let $L$ be the point stabilizer. It means that for every two $k$-tuples of distinct cosets $(Lx_1, \dots, Lx_k)$ and $(Ly_1, \dots, Ly_k)$ there is some $a \in G$ such that $Lx_ia = Ly_i$ for each $1 \leq i \leq k$. That is, $$\bigcap_{i=1}^k x_i^{-1}Ly_i \neq \emptyset.$$ | |
| Jan 7, 2015 at 13:38 | comment | added | HJRW | Algebraically, what does the highly transitive hypothesis mean about a point stabilizer? | |
| Jan 6, 2015 at 12:37 | history | asked | Pablo | CC BY-SA 3.0 |