1University of Michigan, Ann Arbor, USA; Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany 2University of Wisconsin-Madison, Madison, USA
Groups, geometry, and dynamics, Tome 18 (2024) no. 4, pp. 1145-1183
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 2 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 2.
1
University of Michigan, Ann Arbor, USA; Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
2
University of Wisconsin-Madison, Madison, USA
Mitul Islam; Andrew Zimmer. Convex co-compact groups with one-dimensional boundary faces. Groups, geometry, and dynamics, Tome 18 (2024) no. 4, pp. 1145-1183. doi: 10.4171/ggd/812
@article{10_4171_ggd_812,
author = {Mitul Islam and Andrew Zimmer},
title = {Convex co-compact groups with one-dimensional boundary faces},
journal = {Groups, geometry, and dynamics},
pages = {1145--1183},
year = {2024},
volume = {18},
number = {4},
doi = {10.4171/ggd/812},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/812/}
}
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AU - Andrew Zimmer
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