Sublinearly Morse Boundary II: Proper geodesic spaces
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866911964301623296 |
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| author | Qing, Yulan Rafi, Kasra Tiozzo, Giulio |
| author_facet | Qing, Yulan Rafi, Kasra Tiozzo, Giulio |
| contents | We build an analogue of the Gromov boundary for any proper geodesic metric space, hence for any finitely generated group. More precisely, for any proper geodesic metric space $X$ and any sublinear function $κ$, we construct a boundary for $X$, denoted $\mathcal{\partial}_κ X$, that is quasi-isometrically invariant and metrizable. As an application, we show that when $G$ is the mapping class group of a finite type surface, or a relatively hyperbolic group, then with minimal assumptions the Poisson boundary of $G$ can be realized on the $κ$-Morse boundary of $G$ equipped the word metric associated to any finite generating set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_03481 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Sublinearly Morse Boundary II: Proper geodesic spaces Qing, Yulan Rafi, Kasra Tiozzo, Giulio Geometric Topology Dynamical Systems Group Theory 20F65, 37D40, 60J50, 57M60 We build an analogue of the Gromov boundary for any proper geodesic metric space, hence for any finitely generated group. More precisely, for any proper geodesic metric space $X$ and any sublinear function $κ$, we construct a boundary for $X$, denoted $\mathcal{\partial}_κ X$, that is quasi-isometrically invariant and metrizable. As an application, we show that when $G$ is the mapping class group of a finite type surface, or a relatively hyperbolic group, then with minimal assumptions the Poisson boundary of $G$ can be realized on the $κ$-Morse boundary of $G$ equipped the word metric associated to any finite generating set. |
| title | Sublinearly Morse Boundary II: Proper geodesic spaces |
| topic | Geometric Topology Dynamical Systems Group Theory 20F65, 37D40, 60J50, 57M60 |
| url | https://arxiv.org/abs/2011.03481 |