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| Remarks on Thurston’s Construction of Pseudo-Anosov Maps of Riemann Surfaces |
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Citation： |
Chaohui ZHANG∗.Remarks on Thurston’s Construction of Pseudo-Anosov Maps of Riemann Surfaces[J].Chinese Annals of Mathematics B,2008,29(1):85~94 |
| Page view： 1143
Net amount： 666 |
Authors： |
Chaohui ZHANG?; |
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| Abstract： |
It is well known that certain isotopy classes of pseudo-Anosov maps on a Riemann surface
$\wt{S}$ of non-excluded type can be defined through Dehn twists $t\wt{\alpha}$ and $t\wt{\beta}$ along simple closed geodesics $\wt{\alpha}$ and $\wt{\beta}$ on $\wt{S}$, respectively. Let $G$ be the corresponding Fuchsian group acting on the hyperbolic plane ${\Bbb{H}}$ so that ${\Bbb{H}}/G\cong \wt{S}$. For any point $a\in \wt{S}$, define $S=\wt{S}\backslash \{a\}$. In this article, the author gives explicit parabolic elements of $G$ from which he constructs pseudo-Anosov classes on $S$ that can be projected to a given pseudo-Anosov class on $\wt{S}$ obtained from Thurston's construction. |
Keywords： |
Quasiconformal mappings, Riemann surfaces, Teichm¨uller spaces, Mapping classes, Dehn twists, Pseudo-Anosov, Bers fiber spaces |
Classification： |
32G15, 30C60, 30F60 |
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