Relative cohomological dimension of a relatively hyperbolic pair
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908352907313152 |
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| author | Patil, Harsh |
| author_facet | Patil, Harsh |
| contents | We show that the relative cohomological dimension $\cd(G,H)$ of a relatively hyperbolic pair $(G,H)$ is always finite when $G$ is torsion-free. We also show that this dimension is preserved under quasi-isometries, provided that $G$ is torsion-free and the peripheral subgroup $H$ is unconstricted and of type $F_{\infty}$.
As a corollary of our methods, we compute $\cd(G,H)$ in a range of cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04349 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relative cohomological dimension of a relatively hyperbolic pair Patil, Harsh Group Theory We show that the relative cohomological dimension $\cd(G,H)$ of a relatively hyperbolic pair $(G,H)$ is always finite when $G$ is torsion-free. We also show that this dimension is preserved under quasi-isometries, provided that $G$ is torsion-free and the peripheral subgroup $H$ is unconstricted and of type $F_{\infty}$. As a corollary of our methods, we compute $\cd(G,H)$ in a range of cases. |
| title | Relative cohomological dimension of a relatively hyperbolic pair |
| topic | Group Theory |
| url | https://arxiv.org/abs/2505.04349 |