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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.03939 |
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| _version_ | 1866916149173682176 |
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| author | Karrer, Annette Miraftab, Babak Zbinden, Stefanie |
| author_facet | Karrer, Annette Miraftab, Babak Zbinden, Stefanie |
| contents | We study connected components of the Morse boundary and their stabilisers. We introduce the notion of point-convergence and show that if the set of non-singleton connected components of the Morse boundary of a finitely generated group $G$ is point-convergent, then every non-singleton connected component is the (relative) Morse boundary of its stabiliser. The above property only depends on the topology of the Morse boundary and hence is invariant under quasi-isometry. This shows that the topology of the Morse boundary not only carries algebraic information but can be used to detect certain subgroups which in some sense are invariant under quasi-isometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subgroups arising from connected components in the Morse boundary Karrer, Annette Miraftab, Babak Zbinden, Stefanie Group Theory 20F65, 20F67 We study connected components of the Morse boundary and their stabilisers. We introduce the notion of point-convergence and show that if the set of non-singleton connected components of the Morse boundary of a finitely generated group $G$ is point-convergent, then every non-singleton connected component is the (relative) Morse boundary of its stabiliser. The above property only depends on the topology of the Morse boundary and hence is invariant under quasi-isometry. This shows that the topology of the Morse boundary not only carries algebraic information but can be used to detect certain subgroups which in some sense are invariant under quasi-isometry. |
| title | Subgroups arising from connected components in the Morse boundary |
| topic | Group Theory 20F65, 20F67 |
| url | https://arxiv.org/abs/2403.03939 |