Pseudo-Anosov maps and fixed points of boundary homeomorphisms compatible with a Fuchsian group
Zhang, Chaohui
Osaka J. Math., Tome 46 (2009) no. 1, p. 783-798 / Harvested from Project Euclid
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.
Publié le : 2009-09-15
Classification:  32G15,  30C60,  30F60
@article{1256564206,
     author = {Zhang, Chaohui},
     title = {Pseudo-Anosov maps and fixed points of boundary homeomorphisms compatible with a Fuchsian group},
     journal = {Osaka J. Math.},
     volume = {46},
     number = {1},
     year = {2009},
     pages = { 783-798},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1256564206}
}
Zhang, Chaohui. Pseudo-Anosov maps and fixed points of boundary homeomorphisms compatible with a Fuchsian group. Osaka J. Math., Tome 46 (2009) no. 1, pp.  783-798. http://gdmltest.u-ga.fr/item/1256564206/