On coarse embeddings of amenable groups into hyperbolic graphs
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866929327597158400 |
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| author | Tessera, Romain |
| author_facet | Tessera, Romain |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_07205 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On coarse embeddings of amenable groups into hyperbolic graphs Tessera, Romain Group Theory Metric Geometry 20F65, 20F67, 20F18 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. |
| title | On coarse embeddings of amenable groups into hyperbolic graphs |
| topic | Group Theory Metric Geometry 20F65, 20F67, 20F18 |
| url | https://arxiv.org/abs/2010.07205 |