Growth of quasiconvex subgroups
Group Theory
2021-04-05 v3 Geometric Topology
Abstract
We prove that non-elementary hyperbolic groups grow exponentially more quickly than their infinite index quasiconvex subgroups. The proof uses the classical tools of automatic structures and Perron-Frobenius theory. We also extend the main result to relatively hyperbolic groups and cubulated groups. These extensions use the notion of growth tightness and the work of Dahmani, Guirardel, and Osin on rotating families.
Cite
@article{arxiv.1602.08085,
title = {Growth of quasiconvex subgroups},
author = {François Dahmani and David Futer and Daniel T. Wise},
journal= {arXiv preprint arXiv:1602.08085},
year = {2021}
}
Comments
28 pages, 1 figure. v3 is the final version, to appear in Math Proc. Cambridge Philos. Soc