Homotopical stability of pseudo-Anosov diffeomorphisms

Abstract

AbstractWe show that the pseudo-Anosov diflEeomorphisms have a kind of stability even outside their own homotopy class, this generalizes some results of Lewowicz and Handel. As a corollary, we show that two pseudo-Anosov maps, with the same dilatation coefficient, which are semi-conjugate on the π1 level are also semiconjugate as dynamical systems by a map which is a ramified cover.