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

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

2005-09-26

arxiv.org/abs/math/0509592v1

Mathematics

Geometric Topology

10 pages, 3 figures

Scientific paper

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.

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