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Pseudo-Anosov maps and pairs of filling simple closed geodesics on Riemann surfaces | | Chaohui Zhang
; | | Date: |
10 May 2011 | | Abstract: | Let $S$ be a Riemann surface with a puncture $x$. Let $asubset S$ be a
simple closed geodesic. In this paper, we show that for any pseudo-Anosov map
$f$ of $S$ that is isotopic to the identity on $Scup {x}$, $(a, f^m(a))$
fills $S$ for $mgeq 3$. We also study the cases of $0<mleq 2$ and show that
if $(a,f^2(a))$ does not fill $S$, then there is only one geodesic $b$ such
that $b$ is disjoint from both $a$ and $f^2(a)$. In fact, $b=f(a)$ and
${a,f(a)}$ forms the boundary of an $x$-punctured cylinder on $S$. As a
consequence, we show that if $a$ and $f(a)$ are not disjoint. Then $(a,f^m(a))$
for any $mgeq 2$ fills $S$. | | Source: | arXiv, 1105.1844 | | Services: | Forum | Review | PDF | Favorites | |
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