Growth Rate Of Dehn Twist Lattice Points In Teichm\"{u}ller Space

Jiawei Han

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arXiv · 2105.08624

Growth Rate Of Dehn Twist Lattice Points In Teichm\"{u}ller Space

Jiawei Han

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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 contrast we 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 multi-twist lattice points intersecting a closed ball of radius $R$ grows coarsely at least at the rate of $R \cdot e^{\frac{h}{2}R}$.

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BibTeX RIS

Jiawei Han. 2021-05-18. Growth Rate Of Dehn Twist Lattice Points In Teichm\"{u}ller Space. https://arxiv.org/abs/2105.08624

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