Lamplighter-like geometry of groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911763896729600 |
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| author | Genevois, Anthony Tessera, Romain |
| author_facet | Genevois, Anthony Tessera, Romain |
| contents | In this article, we introduce halo products as a natural generalisation of wreath products. They also encompass lampshuffler groups $\mathrm{FSym}(H) \rtimes H$ and lampcloner groups $\mathrm{FGL}(H) \rtimes H$, as well as many possible variations based for instance on braid groups, Thompson's groups, mapping class groups, automorphisms of free groups. We build a geometric framework that allows us to study the large-scale geometry of halo groups, providing refined invariants distinguishing various halo groups up to quasi-isometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13520 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lamplighter-like geometry of groups Genevois, Anthony Tessera, Romain Group Theory Geometric Topology Metric Geometry 20F65, 20F69 In this article, we introduce halo products as a natural generalisation of wreath products. They also encompass lampshuffler groups $\mathrm{FSym}(H) \rtimes H$ and lampcloner groups $\mathrm{FGL}(H) \rtimes H$, as well as many possible variations based for instance on braid groups, Thompson's groups, mapping class groups, automorphisms of free groups. We build a geometric framework that allows us to study the large-scale geometry of halo groups, providing refined invariants distinguishing various halo groups up to quasi-isometry. |
| title | Lamplighter-like geometry of groups |
| topic | Group Theory Geometric Topology Metric Geometry 20F65, 20F69 |
| url | https://arxiv.org/abs/2401.13520 |