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

Boileau, Michel; Ni, Yi; Wang, Shicheng

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

Authors

Boileau, Michel

Ni, Yi

Wang, Shicheng

Description

Let $F',F$ be any two closed orientable surfaces of genus $g'>g\ge 1$, and $f:F\to F$ be any pseudo-Anosov map. Then we can "extend" $f$ to be a pseudo-Anosov map $f':F'\to F'$ so that there is a fiber preserving degree one map $M(F',f')\to M(F,f)$ between the hyperbolic surface bundles. Moreover the extension $f'$ can be chosen so that the surface bundles $M(F',f')$ and $M(F,f)$ have the same first Betti numbers.
10 pages, 3 figures