### Pseudo-Anosov maps and fixed points of boundary homeomorphisms compatible with a Fuchsian group

Chaohui Zhang
Source: Osaka J. Math. Volume 46, Number 3 (2009), 783-798.

#### 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.

First Page:
Primary Subjects: 32G15
Secondary Subjects: 30C60, 30F60
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.ojm/1256564206
Zentralblatt MATH identifier: 05644237
Mathematical Reviews number (MathSciNet): MR2583329

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