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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.00173 |
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| _version_ | 1866914777938264064 |
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| author | Mastrocola, Jill |
| author_facet | Mastrocola, Jill |
| contents | In this paper, we define the 2-complete Artin complex and show that it is systolic for locally reducible Artin groups. The stabilizers of simplices in this complex are exactly the proper parabolic subgroups which are "2-complete." We use this systolicity to show that parabolic subgroups, with 2-completions that are not the whole Artin group, are weakly malnormal. This allows us to conclude that many locally reducible Artin groups are acylindrically hyperbolic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00173 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Negative curvature in locally reducible Artin groups Mastrocola, Jill Group Theory In this paper, we define the 2-complete Artin complex and show that it is systolic for locally reducible Artin groups. The stabilizers of simplices in this complex are exactly the proper parabolic subgroups which are "2-complete." We use this systolicity to show that parabolic subgroups, with 2-completions that are not the whole Artin group, are weakly malnormal. This allows us to conclude that many locally reducible Artin groups are acylindrically hyperbolic. |
| title | Negative curvature in locally reducible Artin groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2405.00173 |