Growth Of Dehn Twist and Pseudo-Anosov Conjugacy Classes in Teichmüller Space
dc.contributor.advisor | Dowdall, Spencer | |
dc.creator | Han, Jiawei | |
dc.date.accessioned | 2022-01-10T16:44:46Z | |
dc.date.created | 2021-12 | |
dc.date.issued | 2021-11-02 | |
dc.date.submitted | December 2021 | |
dc.identifier.uri | http://hdl.handle.net/1803/16962 | |
dc.description.abstract | Athreya, Bufetov, Eskin and Mirzakhani have shown the number of mapping class group lattice points intersecting a closed ball of radius $R$ in Teichm\"{u}ller space is asymptotic to $e^{hR}$, where $h$ is the dimension of the Teichm\"{u}ller space. In this thesis, we first show the number of Dehn twist lattice points intersecting a closed ball of radius $R$ is coarsely asymptotic to $e^{\frac{h}{2}R}$. Moreover, we show the number of all multi-twists lattice points intersecting a closed ball of radius $R$ grows coarsely at least at the rate of $R \cdot e^{\frac{h}{2}R}$. Furthermore, we show for any pseudo-Anosov mapping class $f$, there exists a power $n$, such that the number of lattice points of the $f^n$ conjugacy class intersecting a closed ball of radius $R$ is coarsely asymptotic to $e^{\frac{h}{2}R}$. | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.subject | Mapping Class Group | |
dc.subject | Teichmuller Space | |
dc.subject | Lattice Point Asymptotics | |
dc.title | Growth Of Dehn Twist and Pseudo-Anosov Conjugacy Classes in Teichmüller Space | |
dc.type | Thesis | |
dc.date.updated | 2022-01-10T16:44:46Z | |
dc.type.material | text | |
thesis.degree.name | PhD | |
thesis.degree.level | Doctoral | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University Graduate School | |
local.embargo.terms | 2023-12-01 | |
local.embargo.lift | 2023-12-01 | |
dc.creator.orcid | 0000-0002-1536-9201 | |
dc.contributor.committeeChair | Dowdall, Spencer |
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