Groups admitting Wirtinger presentations and Gromov hyperbolic groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914068917387264 |
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| author | Akita, Toshiyuki |
| author_facet | Akita, Toshiyuki |
| contents | Twisted Wirtinger presentations are generalizations of the classical Wirtinger presentations of knot and link groups. In this paper, we prove that if a finitely generated group admitting a twisted Wirtinger presentation is Gromov hyperbolic, then its second rational homology group vanishes. Moreover, if the group is torsion-free, then its second integral homology group also vanishes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07143 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Groups admitting Wirtinger presentations and Gromov hyperbolic groups Akita, Toshiyuki Group Theory Geometric Topology Primary 20F05, 20F67, 20J06, Secondary 20F65 Twisted Wirtinger presentations are generalizations of the classical Wirtinger presentations of knot and link groups. In this paper, we prove that if a finitely generated group admitting a twisted Wirtinger presentation is Gromov hyperbolic, then its second rational homology group vanishes. Moreover, if the group is torsion-free, then its second integral homology group also vanishes. |
| title | Groups admitting Wirtinger presentations and Gromov hyperbolic groups |
| topic | Group Theory Geometric Topology Primary 20F05, 20F67, 20J06, Secondary 20F65 |
| url | https://arxiv.org/abs/2506.07143 |