Inventiones mathematicae

, Volume 87, Issue 1, pp 129-151

First online:

Dehn twists and pseudo-Anosov diffeomorphisms

  • Albert FathiAffiliated withDépartement de Mathématique, UA 1169 du CNRS, Université Paris-Sud

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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 γ n f contains a pseudo-Anosov diffeomorphism except for at most 7 consecutive values ofn.