Property $R_{\infty}$ for groups with infinitely many ends
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866910034412175360 |
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| author | Fournier-Facio, Francesco Iveson, Harry Martino, Armando Sgobbi, Wagner Wong, Peter |
| author_facet | Fournier-Facio, Francesco Iveson, Harry Martino, Armando Sgobbi, Wagner Wong, Peter |
| contents | We show that an accessible group with infinitely many ends has property $R_{\infty}$. That is, it has infinitely many twisted conjugacy classes for any twisting automorphism. We deduce that having property $R_{\infty}$ is undecidable amongst finitely presented groups.
We also show that the same is true for a wide class of relatively hyperbolic groups, filling in some of the gaps in the literature. Specifically, we show that a non-elementary, finitely presented relatively hyperbolic group with finitely generated peripheral subgroups which are not themselves relatively hyperbolic, has property $R_{\infty}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12002 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Property $R_{\infty}$ for groups with infinitely many ends Fournier-Facio, Francesco Iveson, Harry Martino, Armando Sgobbi, Wagner Wong, Peter Group Theory Geometric Topology We show that an accessible group with infinitely many ends has property $R_{\infty}$. That is, it has infinitely many twisted conjugacy classes for any twisting automorphism. We deduce that having property $R_{\infty}$ is undecidable amongst finitely presented groups. We also show that the same is true for a wide class of relatively hyperbolic groups, filling in some of the gaps in the literature. Specifically, we show that a non-elementary, finitely presented relatively hyperbolic group with finitely generated peripheral subgroups which are not themselves relatively hyperbolic, has property $R_{\infty}$. |
| title | Property $R_{\infty}$ for groups with infinitely many ends |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2504.12002 |