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arXiv · 2310.03644

Failure of quasi-isometric rigidity for infinite-ended groups

Nir Lazarovich·Emily Stark
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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.

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Nir Lazarovich, Emily Stark. 2023-10-05. Failure of quasi-isometric rigidity for infinite-ended groups. https://arxiv.org/abs/2310.03644

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