The quasi-redirecting Boundary
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929397992259584 |
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| author | Qing, Yulan Rafi, Kasra |
| author_facet | Qing, Yulan Rafi, Kasra |
| contents | We generalize the notion of Gromov boundary to a larger class of metric spaces beyond Gromov hyperbolic spaces. Points in this boundary are classes of quasi-geodesic rays and the space is equipped with a topology that is naturally invariant under quasi-isometries. It turns out that this boundary is compatible with other notions of boundary in many ways; it contains the sublinearly Morse boundary as a topological subspace and it matches the Bowditch boundary of relative hyperbolic spaces when the peripheral subgroups have no intrinsic hyperbolicity. We also give a complete description of the boundary of the Croke-Kleiner group where the quasi-redirecting boundary reveals a new class of QI-invariant, Morse-like quasi-geodesics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16794 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The quasi-redirecting Boundary Qing, Yulan Rafi, Kasra Group Theory 20F65, 57M60 We generalize the notion of Gromov boundary to a larger class of metric spaces beyond Gromov hyperbolic spaces. Points in this boundary are classes of quasi-geodesic rays and the space is equipped with a topology that is naturally invariant under quasi-isometries. It turns out that this boundary is compatible with other notions of boundary in many ways; it contains the sublinearly Morse boundary as a topological subspace and it matches the Bowditch boundary of relative hyperbolic spaces when the peripheral subgroups have no intrinsic hyperbolicity. We also give a complete description of the boundary of the Croke-Kleiner group where the quasi-redirecting boundary reveals a new class of QI-invariant, Morse-like quasi-geodesics. |
| title | The quasi-redirecting Boundary |
| topic | Group Theory 20F65, 57M60 |
| url | https://arxiv.org/abs/2406.16794 |