Failure of quasi-isometric rigidity for infinite-ended groups
Group Theory
2023-10-06 v1 Geometric Topology
Abstract
We prove that an infinite-ended group whose one-ended factors have finite-index subgroups and are in a family of groups with a nonzero multiplicative invariant is not quasi-isometrically rigid. Combining this result with work of the first author proves that a residually-finite multi-ended hyperbolic group is quasi-isometrically rigid if and only if it is virtually free. The proof adapts an argument of Whyte for commensurability of free products of closed hyperbolic surface groups.
Keywords
Cite
@article{arxiv.2310.03644,
title = {Failure of quasi-isometric rigidity for infinite-ended groups},
author = {Nir Lazarovich and Emily Stark},
journal= {arXiv preprint arXiv:2310.03644},
year = {2023}
}
Comments
8 pages