5 papers
Non-arithmeticity of length spectra of subgroups of mapping class groups
Inhyeok Choi, Dongryul M. Kim
In this paper, we prove that every non-elementary subgroup of the mapping class group of a surface has non-arithmetic Teichmüller length spectrum. Namely, Teichmüller translation…
Divergence-type semigroups in Kleinian groups and Hausdorff dimension
Inhyeok Choi
Let be a non-elementary, non-convex-cocompact Kleinian group acting on . We show that the Hausdorff dimension of the sublinearly conical Myrberg limit set of $…
Counting pseudo-Anosovs as weakly contracting isometries
Inhyeok Choi
We show that pseudo-Anosov mapping classes are generic in every Cayley graph of the mapping class group of a finite-type hyperbolic surface. Our method also yields an analogous res…
Contracting isometries and differentiability of the escape rate
Inhyeok Choi
Let be a countable group whose action on a metric space involves a contracting isometry. This setting naturally encompasses groups acting on Gromov hyperbolic spaces, Teich…
Smoothing countable group actions on metrizable spaces
Inhyeok Choi, Sang-hyun Kim
We prove that every topological action of a countable group on a metrizable space can be realized as a bi-Lipschitz action with respect to some compatible metric. This extends a re…