Characterizations of Stability via Morse Limit Sets
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909973976449024 |
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| author | Garcia, Jacob |
| author_facet | Garcia, Jacob |
| contents | Subgroup stability is a strong notion of quasiconvexity that generalizes convex cocompactness in a variety of settings. In this paper, we characterize stability of a subgroup by properties of its limit set on the Morse boundary. Given $H<G$, both finitely generated, $H$ is stable exactly when all the limit points of $H$ are conical, or equivalently when all the limit points of $H$ are horospherical, as long as the limit set of $H$ is a compact subset of the Morse boundary for $G$. We also demonstrate an application of these results in the settings of the mapping class group for a finite type surface, $\text{Mod}(S)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09135 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Characterizations of Stability via Morse Limit Sets Garcia, Jacob Metric Geometry Group Theory Geometric Topology Subgroup stability is a strong notion of quasiconvexity that generalizes convex cocompactness in a variety of settings. In this paper, we characterize stability of a subgroup by properties of its limit set on the Morse boundary. Given $H<G$, both finitely generated, $H$ is stable exactly when all the limit points of $H$ are conical, or equivalently when all the limit points of $H$ are horospherical, as long as the limit set of $H$ is a compact subset of the Morse boundary for $G$. We also demonstrate an application of these results in the settings of the mapping class group for a finite type surface, $\text{Mod}(S)$. |
| title | Characterizations of Stability via Morse Limit Sets |
| topic | Metric Geometry Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2309.09135 |