Automorphism and outer automorphism groups of Right-angled Artin groups are not relatively hyperbolic
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916164435705856 |
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| author | Kim, Junseok Oh, Sangrok Tranchida, Philippe |
| author_facet | Kim, Junseok Oh, Sangrok Tranchida, Philippe |
| contents | We show that the automorphism groups of right-angled Artin groups whose defining graphs have at least 3 vertices are not relatively hyperbolic. We then show that the outer automorphism groups are not relatively hyperbolic, if they are not virtually isomorphic to a right-angled Artin group whose defining graph is either a single vertex or disconnected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_14760 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Automorphism and outer automorphism groups of Right-angled Artin groups are not relatively hyperbolic Kim, Junseok Oh, Sangrok Tranchida, Philippe Group Theory Geometric Topology We show that the automorphism groups of right-angled Artin groups whose defining graphs have at least 3 vertices are not relatively hyperbolic. We then show that the outer automorphism groups are not relatively hyperbolic, if they are not virtually isomorphic to a right-angled Artin group whose defining graph is either a single vertex or disconnected. |
| title | Automorphism and outer automorphism groups of Right-angled Artin groups are not relatively hyperbolic |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2104.14760 |