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Mathematics > Group Theory
Title: On coarse embeddings of amenable groups into hyperbolic graphs
(Submitted on 14 Oct 2020 (v1), last revised 26 Apr 2024 (this version, v3))
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.
Submission history
From: Romain Tessera [view email][v1] Wed, 14 Oct 2020 16:20:52 GMT (6kb)
[v2] Wed, 14 Dec 2022 10:19:31 GMT (7kb)
[v3] Fri, 26 Apr 2024 09:09:37 GMT (10kb)
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