Abstract
Let S be a Riemann surface of type (p, n) with 3p + n > 4 and n ≥ 1. Let a be a puncture of S. We show that for any Dehn twist tc along a simple closed geodesic c on S, there exists a sequence {fm} of pseudo-Anosov maps of S such that for sufficiently large integers m, the products fm $\circ$ tck are pseudo-Anosov for all integers k. As a corollary, we prove that for a multi-twist M2 on $\tilde{S}$ along two disjoint simple closed geodesics, there are infinitely many pseudo-Anosov maps of S that are isotopic to M2 as a is filled in.
Citation
Chaohui Zhang. "Dehn twists combined with pseudo-Anosov maps." Kodai Math. J. 34 (3) 367 - 382, October 2011. https://doi.org/10.2996/kmj/1320935547
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