Pseudo-Anosov mapping classes and their representations by products of two Dehn twists

被引：0

作者：

Chaohui Zhang

机构：

[1] Morehouse College,Department of Mathematics

来源：

Chinese Annals of Mathematics, Series B | 2009年 / 30卷

关键词：

Riemann surface; Pseudo-Anosov map; Dehn twist; Teichmüller space; Bers fiber space; 32G15; 30C60; 30F60;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \tilde S $$\end{document} be a Riemann surface of analytically finite type (p, n) with 3p − 3 + n > 0. Let a ∈ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \tilde S $$\end{document} and S = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \tilde S $$\end{document} − {a}. In this article, the author studies those pseudo-Anosov maps on S that are isotopic to the identity on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \tilde S $$\end{document} and can be represented by products of Dehn twists. It is also proved that for any pseudo-Anosov map f of S isotopic to the identity on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \tilde S $$\end{document}, there are infinitely many pseudo-Anosov maps F on S − {b} = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \tilde S $$\end{document} − {a, b}, where b is a point on S, such that F is isotopic to f on S as b is filled in.

引用

页码：281 / 292

页数：11

共 18 条

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