Pseudo-Anosov extensions and degree one maps between hyperbolic surface bundles

Michel Boileau, Yi Ni, Shicheng Wang

Let $F^{\prime },F$ be any two closed orientable surfaces of genus $g^{\prime }>g\ge 1$, and $f:F\to F$ be any pseudo-Anosov map. Then we can "extend" $f$ to be a pseudo-Anosov map $f^{\prime }:F^{\prime }\to F^{\prime }$ so…