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On representations of certain pseudo-Anosov maps of Riemann surfaces with puncture | | Chaohui Zhang
; | | Date: |
28 Aug 2007 | | Abstract: | Let $S$ be a Riemann surface of type $(p,n)$ with $3p+n>4$ and $ngeq 1$. Let
$alpha_1,alpha_2subset S$ be two simple closed geodesics such that
${alpha_1, alpha_2}$ fills $S$. It was shown by Thurston that most maps
obtained through Dehn twists along $alpha_1$ and $alpha_2$ are pseudo-Anosov.
Let $a$ be a puncture. In this paper, we study the family $mathcal{F}(S,a)$ of
pseudo-Anosov maps on $S$ that projects to the trivial map as $a$ is filled in,
and show that there are infinitely many elements in $mathcal{F}(S,a)$ that
cannot be obtained from Dehn twists along two filling geodesics. We further
characterize all elements in $mathcal{F}(S,a)$ that can be constructed by two
filling geodesics. Finally, for any point $bin S$, we obtain a family
$mathcal{H}$ of pseudo-Anosov maps on $Sackslash {b}$ that is not obtained
from Thurston’s construction and projects to an element $chiin
mathcal{F}(S,a)$ as $b$ is filled in, some properties of elements in
$mathcal{H}$ are also discussed. | | Source: | arXiv, 0708.3685 | | Services: | Forum | Review | PDF | Favorites | |
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