Growth of pseudo-Anosov conjugacy classes in Teichmüller space

IF 0.6 3区数学 Q3 MATHEMATICS

Groups Geometry and Dynamics Pub Date : 2021-05-18 DOI:10.4171/ggd/724

Jiawei Han

引用次数: 1

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. 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 $e^{\frac{h}{2}R}$.

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Teichmüller空间中拟Anosov共轭类的增长

Athreya, Bufetov, Eskin和Mirzakhani证明了在Teichm\ {u}ller空间中与半径$R$的闭球相交的映射类群格点的个数渐近于$e^{hR}$，其中$h$是Teichm\ {u}ller空间的维数。我们证明了对于任意伪anosov映射类$f$，存在一个幂$n$，使得$f^n$共轭类与半径$R$的闭球相交的格点数大致渐近于$e^{\frac{h}{2}R}$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Groups Geometry and Dynamics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Groups, Geometry, and Dynamics is devoted to publication of research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. The journal covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields. Topics covered include: geometric group theory; asymptotic group theory; combinatorial group theory; probabilities on groups; computational aspects and complexity; harmonic and functional analysis on groups, free probability; ergodic theory of group actions; cohomology of groups and exotic cohomologies; groups and low-dimensional topology; group actions on trees, buildings, rooted trees.