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arXiv · 1407.1107

Bilipschitz versus quasi-isometric equivalence for higher rank lamplighter groups

Tullia Dymarz·Irine Peng·Jennifer Taback
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Abstract

We describe a family of finitely presented groups which are quasi-isometric but not bilipschitz equivalent. The first such examples were described by the first author and are the lamplighter groups $F \wr \mathbb{Z}$ where $F$ is a finite group; these groups are finitely generated but not finitely presented. The examples presented in this paper are higher rank generalizations of these lamplighter groups and include groups that are of type $F_n$ for any $n$.

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Tullia Dymarz, Irine Peng, Jennifer Taback. 2014-07-04. Bilipschitz versus quasi-isometric equivalence for higher rank lamplighter groups. https://arxiv.org/abs/1407.1107

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