Convex co-compact groups with one dimensional boundary faces
Geometric Topology
2024-07-31 v2 Differential Geometry
Group Theory
Metric Geometry
Abstract
In this paper we consider convex co-compact subgroups of the projective linear group. We prove that such a group is relatively hyperbolic with respect to a collection of virtually Abelian subgroups of rank two if and only if each open face in the ideal boundary has dimension at most one. We also introduce the "coarse Hilbert dimension" of a subset of a convex set and use it to characterize when a naive convex co-compact subgroup is word hyperbolic or relatively hyperbolic with respect to a collection of virtually Abelian subgroups of rank two.
Cite
@article{arxiv.2104.05056,
title = {Convex co-compact groups with one dimensional boundary faces},
author = {Mitul Islam and Andrew Zimmer},
journal= {arXiv preprint arXiv:2104.05056},
year = {2024}
}
Comments
v2: Minor revisions based on referees' reports. To appear in Groups, Geometry, and Dynamics. 32 pages. Comments welcome. arXiv admin note: text overlap with arXiv:1910.08885