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May
8 |
awarded | Yearling |
Sep
13 |
awarded | Necromancer |
Jul
2 |
awarded | Curious |
May
8 |
awarded | Yearling |
Dec
11 |
comment |
An example of a non-amenable exact group without free subgroups.
I don't think the group above is known to be exact. |
Nov
20 |
answered | Uniform bounds on Kazhdan constants in groups |
Nov
20 |
comment |
Uniform bounds on Kazhdan constants in groups
It seems so, by Gelander and Zuk ams.org/mathscinet/search/… |
Nov
15 |
comment |
Folner sets and balls
Thanks so much for this beautiful post! Accidentally, I also analyzed this presentation (and I'm an old fan of the combinatorial hyperbolic plane). I need to think more about your intuition concerning arbitrarly generating sets. |
Nov
15 |
comment |
Folner sets and balls
In general a free semigroup won't help you that much, since you need both lower and upper bounds estimation on the sizes of balls... |
Nov
15 |
comment |
Folner sets and balls
It looks unlikely, nevertheless, I don't have a disproof. In fact, the shape of Folner sets in exponential growth groups is quite unclear to me, so I asked the most basic question I could come up with. I have no decent evidence for or against, but often enough the quantity $liminf c_{n+1}/c_n$, where $c_n$ is the size of the ball, is less than the growth... so it is not clear so far. |
Nov
15 |
comment |
Folner sets and balls
Thanks for the comment. A sequence of balls in my phrasing was meant to be a subsequence of the sequence of the balls, indeed. I hope it is clear. |
Nov
15 |
revised |
Folner sets and balls
edited body |
Nov
15 |
asked | Folner sets and balls |
Nov
6 |
awarded | Nice Answer |
Nov
4 |
answered | Is there an infinite group with exactly two conjugacy classes? |
Oct
19 |
answered | New trends in Applied Graph Theory |
Oct
9 |
awarded | Caucus |
Oct
9 |
answered | Rotation numbers for amenable group actions on the circle |
Oct
1 |
comment |
Speed of random walks in groups
You re welcome. Very interesting, I don´t know any reference or proof... I might think about it, maybe there is a simple reason for it. I let you know if I succeed. Dan |
Sep
4 |
awarded | Enthusiast |