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| Pseudo-Anosov Mapping Classes and Their Representations by Products of Two Dehn Twists |
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Citation： |
Chaohui ZHANG.Pseudo-Anosov Mapping Classes and Their Representations by Products of Two Dehn Twists[J].Chinese Annals of Mathematics B,2009,30(3):281~292 |
| Page view： 1640
Net amount： 1616 |
Authors： |
Chaohui ZHANG; |
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| Abstract： |
Let $\wt S$ be a Riemann surface of analytically finite type $(p,n)$
with $3p-3+n>0$. Let $a\in\wt S$ and $S=\wt S-\{a\}$. In this
article, the author studies those pseudo-Anosov maps on $S$ that are
isotopic to the identity on $\wt S$ and can be represented by
products of Dehn twists. It is also proved that for any
pseudo-Anosov map $f$ of $S$ isotopic to the identity on $\wt S$,
there are infinitely many pseudo-Anosov maps F on $S-\{b\}=\wt S
-\{a, b\}$, where $b$ is a point on $S$, such that $F$ is isotopic
to $f$ on $S$ as $b$ is filled in. |
Keywords： |
Riemann surface, Pseudo-Anosov map, Dehn twist, Teichm¨uller
space, Bers fiber space |
Classification： |
32G15, 30C60, 30F60 |
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