All Questions
Tagged with geometric-group-theory ds.dynamical-systems
9 questions with no upvoted or accepted answers
7
votes
0
answers
286
views
Hyperbolic group with boundary $S^1$ implies virtually Fuchsian via bounded cohomology?
Question: Is there an approach to $\partial G \cong S^1$ implies virtually Fuchsian using bounded cohomology of $\mathrm{Homeo^+} (S^1)$? If not is there a reason to believe it wouldn't work, or maybe ...
user35370
6
votes
0
answers
355
views
Arithmetic Teichmüller curves, first eigenvalue of the Laplacian, McMullen's expander conjecture
$\DeclareMathOperator\SL{SL}$By a result due to Ellenberg and McReynolds, any finite index subgroup $\Gamma$ of $\Gamma(2) \subset \SL\left(2,\mathbb{Z}\right)$ is the Veech group of an arithmetic ...
- 31
6
votes
0
answers
108
views
Stable commutator lengths of pseudo-Anosovs
Does anyone have an example of a pseudo-Anosov mapping class for which the stable commutator length is known exactly?
- 61
5
votes
0
answers
155
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Are there examples of hyperbolic manifolds with finite Bowen-Margulis measure and fundamental group which is not relatively hyperbolic?
It is well known that a geometrically finite hyperbolic manifold (quotient of $H^n$) has finite Bowen-Margulis measure.
Marc Peigné [1] constructed examples of geometrically infinite hyperbolic ...
- 481
3
votes
0
answers
157
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Question about martin boundaries of random walks induced on transient subgroups
Suppose $\Gamma$ is a discrete, finitely generated, non-amenable group, and
consider a random walk given by a measure $\mu$.
Assume the measure is symmetric, finitely generated, and the support of
$\...
- 2,964
3
votes
0
answers
383
views
Discontinuity of Radon-Nikodym derivative for Patterson-Sullivan measures for word metrics on Gromov hyperbolic groups
Let $\Gamma$ be a Gromov hyperbolic group coming endowed with a word metric coming from some finite generating set. Let $\nu$ be an associated Patterson-Sullivan measure (quasi-conformal density).
I ...
- 2,964
2
votes
0
answers
153
views
Proof of Zimmer's cocycle super-rigidity theorem
I was reading the proof of Zimmer's cocycle super-rigidity theorem from the book 'Ergodic theory and semi-simple groups' by Robert Zimmer (Theorem 5.2.5, page 98). But I am not able to understand it. ...
- 331
2
votes
0
answers
87
views
Hausdorff dimension of radial limit sets for divergence type subgroups
Let $X$ be a proper $CAT(-1)$ space.
Let $\Gamma<Isom(X)$ be a subgroup of divergence type.
Is it true that the Hausdorff dimension of the radial limit set of $\Gamma$ in $\partial X$ is equal to ...
- 2,964
1
vote
0
answers
107
views
Relations between $\Omega$-groups, locally indicable groups, and right-orderable groups
We know that the class of right-orderable groups $\mathit{RO}$, is contained in the class of $\Omega$-groups (read it from "A note on group rings of certain torsion-free groups" by Burns-Hale).
A ...
- 51