Sigma-compactness of Morse boundaries in Morse local-to-global groups and applications to stationary measures
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916337530437632 |
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| author | He, Vivian Spriano, Davide Zbinden, Stefanie |
| author_facet | He, Vivian Spriano, Davide Zbinden, Stefanie |
| contents | We show that the Morse boundary of a Morse local-to-global group is $σ$-compact. Moreover, we show that the converse holds for small cancellation groups. As an application, we show that the Morse boundary of a non-hyperbolic, Morse local-to-global group that has contraction does not admit a non-trivial stationary measure. In fact, we show that any stationary measure on a geodesic boundary of such a groups needs to assign measure zero to the Morse boundary. Unlike previous results, we do not need any assumptions on the stationary measures considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18863 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sigma-compactness of Morse boundaries in Morse local-to-global groups and applications to stationary measures He, Vivian Spriano, Davide Zbinden, Stefanie Group Theory Metric Geometry 20F65 We show that the Morse boundary of a Morse local-to-global group is $σ$-compact. Moreover, we show that the converse holds for small cancellation groups. As an application, we show that the Morse boundary of a non-hyperbolic, Morse local-to-global group that has contraction does not admit a non-trivial stationary measure. In fact, we show that any stationary measure on a geodesic boundary of such a groups needs to assign measure zero to the Morse boundary. Unlike previous results, we do not need any assumptions on the stationary measures considered. |
| title | Sigma-compactness of Morse boundaries in Morse local-to-global groups and applications to stationary measures |
| topic | Group Theory Metric Geometry 20F65 |
| url | https://arxiv.org/abs/2407.18863 |