Twisted right-angled Artin groups embedded in knot groups
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913599137513472 |
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| author | Himeno, Keisuke Teragaito, Masakazu |
| author_facet | Himeno, Keisuke Teragaito, Masakazu |
| contents | Twisted right-angled Artin groups are defined through presentation based on mixed graphs. Each vertex corresponds to a generator, each undirected edge yields a commuting relation and each directed edge gives a Klein bottle relation. If there is no directed edge, then this reduces to an ordinary right-angled Artin group.
There is a characterization of right-angled Artin groups which can be embedded in knot groups by Katayama. In this paper, we completely determine twisted right-angled Artin groups embedded in knot groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03849 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted right-angled Artin groups embedded in knot groups Himeno, Keisuke Teragaito, Masakazu Geometric Topology Group Theory 20F36, 57K10 Twisted right-angled Artin groups are defined through presentation based on mixed graphs. Each vertex corresponds to a generator, each undirected edge yields a commuting relation and each directed edge gives a Klein bottle relation. If there is no directed edge, then this reduces to an ordinary right-angled Artin group. There is a characterization of right-angled Artin groups which can be embedded in knot groups by Katayama. In this paper, we completely determine twisted right-angled Artin groups embedded in knot groups. |
| title | Twisted right-angled Artin groups embedded in knot groups |
| topic | Geometric Topology Group Theory 20F36, 57K10 |
| url | https://arxiv.org/abs/2412.03849 |