Path-connectivity of Thick Laminations, and Markov Processes with Thick Limit Sets
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929567501910016 |
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| author | Chaika, Jon Hensel, Sebastian |
| author_facet | Chaika, Jon Hensel, Sebastian |
| contents | A lamination $λ$ is $ε$-thick (with respect to a basepoint $X$), if the Teichmüller ray from $X$ in the direction of $λ$ stays in the $ε$-thick part. We show that, for surfaces of high enough genus, any two $ε$-thick laminations can be joined by a path of $δ$-thick laminations. As a consequence, we show that the Morse boundary of the mapping class group is path-connected. Furthermore, we construct a subshift of finite type on the mapping class group, whose limit set consists only of thick laminations and is path-connected. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_22518 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Path-connectivity of Thick Laminations, and Markov Processes with Thick Limit Sets Chaika, Jon Hensel, Sebastian Geometric Topology Group Theory A lamination $λ$ is $ε$-thick (with respect to a basepoint $X$), if the Teichmüller ray from $X$ in the direction of $λ$ stays in the $ε$-thick part. We show that, for surfaces of high enough genus, any two $ε$-thick laminations can be joined by a path of $δ$-thick laminations. As a consequence, we show that the Morse boundary of the mapping class group is path-connected. Furthermore, we construct a subshift of finite type on the mapping class group, whose limit set consists only of thick laminations and is path-connected. |
| title | Path-connectivity of Thick Laminations, and Markov Processes with Thick Limit Sets |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2410.22518 |