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Some pseudo-Anosov maps on punctured Riemann surfaces represented by multi-twist | | Chaohui Zhang
; | | Date: |
6 Aug 2007 | | Abstract: | Let A, B be families of disjoint non-trivial simple closed geodesics on a
Riemann surface S so that each component of $Sackslash {Acup B}$ is either
a disk or a once punctured disk. Let w be any word consisting of Dehn twists
along elements of A and inverses of Dehn twists along elements of B so that the
Dehn twist along each element of A and the inverse of the Dehn twist along each
element of B occur at least once in w. It is well known that w represents a
pseudo-Anosov class. In this paper we study those pseudo-Anosov maps f on S
projecting to the trivial map as a puncture a is filled in. We prove the
following theorem. Let S be of type (p,n), 3p-4+n>0 and $ngeq 1$. Write
$A={alpha_1,..., alpha_k}$, $kgeq 1$. If all $alpha_i$ are non-trivial
and distinct as geodesics on $ ilde{S}=Scup {a}$, then for any integer
tuples (n_1,..., n_k), the composition $t_{alpha_1}^{n_1}circ ... circ
t_{alpha_k}^{n_k}circ f$ is also a pseudo-Anosov map. As a consequence we
also prove that if S is of type (p,1) with $pgeq 2$, then for every integer m,
f^m is not isotopic to any word w described above. | | Source: | arXiv, 0708.0804 | | Services: | Forum | Review | PDF | Favorites | |
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