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September 2009 Pseudo-Anosov maps and fixed points of boundary homeomorphisms compatible with a Fuchsian group
Chaohui Zhang
Osaka J. Math. 46(3): 783-798 (September 2009).

Abstract

Let $\tilde{S}$ be a Riemann surface of type $(p,n)$ with $3p-3+n>0$. Let $F$ be a pseudo-Anosov map of $\tilde{S}$ defined by two filling simple closed geodesics on $\tilde{S}$. Let $a\in \tilde{S}$, and $S=\tilde{S} - \{a\}$. For any map $f\colon S\to S$ that is generated by two simple closed geodesics and is isotopic to $F$ on $\tilde{S}$, there corresponds to a configuration $\tau$ of invariant half planes in the universal covering space of $\tilde{S}$. We give a necessary and sufficient condition (with respect to the configuration) for those $f$ to be pseudo-Anosov maps. As a consequence, we obtain infinitely many pseudo-Anosov maps $f$ on $S$ that are isotopic to $F$ on $\tilde{S}$ as $a$ is filled in.

Citation

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Chaohui Zhang. "Pseudo-Anosov maps and fixed points of boundary homeomorphisms compatible with a Fuchsian group." Osaka J. Math. 46 (3) 783 - 798, September 2009.

Information

Published: September 2009
First available in Project Euclid: 26 October 2009

zbMATH: 1179.30048
MathSciNet: MR2583329

Subjects:
Primary: 32G15
Secondary: 30C60, 30F60

Rights: Copyright © 2009 Osaka University and Osaka City University, Departments of Mathematics

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Vol.46 • No. 3 • September 2009
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