Summary
We show that it is possible to obtain many pseudo-Anosov diffeomorphisms from Dehn twists. In particular, we generalize a theorem of Long and Morton to obtain that iff is a pseudo-Anosov diffeomorphism of an oriented surface andT γ is the Dehn twist around the simple closed curve γ, then the isotopy class ofT nγ f contains a pseudo-Anosov diffeomorphism except for at most 7 consecutive values ofn.
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Fathi, A. Dehn twists and pseudo-Anosov diffeomorphisms. Invent Math 87, 129–151 (1987). https://doi.org/10.1007/BF01389156
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DOI: https://doi.org/10.1007/BF01389156