A Characterization of Relative Hyperbolicity via Morse and Contracting Boundaries
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917359617310720 |
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| author | PT, Vyshnav Sardar, Pranab Sardar, Rana |
| author_facet | PT, Vyshnav Sardar, Pranab Sardar, Rana |
| contents | We prove the following boundary-theoretic characterization of relatively hyperbolic groups. Let $G$ be a finitely generated group with a finite collection $\mathcal{H}$ of finitely generated subgroups, and let $G^h$ denote the associated cusped space. We prove that the pair $(G,\mathcal{H})$ is non-elementary relatively hyperbolic if and only if the Morse boundary $\partial_M^{\mathcal{DL}} G^h$ or the contracting boundary $\partial_c^{\mathcal{FQ}} G^h$ is non-empty and compact. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_23141 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Characterization of Relative Hyperbolicity via Morse and Contracting Boundaries PT, Vyshnav Sardar, Pranab Sardar, Rana Geometric Topology 20F65, 20F67 We prove the following boundary-theoretic characterization of relatively hyperbolic groups. Let $G$ be a finitely generated group with a finite collection $\mathcal{H}$ of finitely generated subgroups, and let $G^h$ denote the associated cusped space. We prove that the pair $(G,\mathcal{H})$ is non-elementary relatively hyperbolic if and only if the Morse boundary $\partial_M^{\mathcal{DL}} G^h$ or the contracting boundary $\partial_c^{\mathcal{FQ}} G^h$ is non-empty and compact. |
| title | A Characterization of Relative Hyperbolicity via Morse and Contracting Boundaries |
| topic | Geometric Topology 20F65, 20F67 |
| url | https://arxiv.org/abs/2603.23141 |