Osaka Journal of Mathematics

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

Chaohui Zhang

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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.

Article information

Osaka J. Math., Volume 46, Number 3 (2009), 783-798.

First available in Project Euclid: 26 October 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]
Secondary: 30C60 30F60: Teichmüller theory [See also 32G15]


Zhang, Chaohui. Pseudo-Anosov maps and fixed points of boundary homeomorphisms compatible with a Fuchsian group. Osaka J. Math. 46 (2009), no. 3, 783--798.

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