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arXiv · 2010.07205

On coarse embeddings of amenable groups into hyperbolic graphs

Romain Tessera
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Abstract

In this note we prove that if a finitely generated amenable group admits a regular map to a direct product of a hyperbolic space and a euclidean space, then it must be virtually nilpotent. We deduce that an amenable group regularly embeds into a hyperbolic group if and only if it is virtually nilpotent, answering a question of Hume and Sisto. We describe an application to Lorentz geometry due to Charles Frances.

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Romain Tessera. 2024-04-26. On coarse embeddings of amenable groups into hyperbolic graphs. https://arxiv.org/abs/2010.07205

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