Pseudo-Anosov extensions and degree one maps between hyperbolic surface bundles
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چکیده
Let F ′,F be any two closed orientable surfaces of genus g′ > g ≥ 1, and f : F → F be any pseudo-Anosov map. Then we can “extend” f to be a pseudoAnosov map f ′ : F ′ → F ′ so that there is a fiber preserving degree one map M(F ′, f ′) → M(F, f ) between the hyperbolic surface bundles. Moreover the extension f ′ can be chosen so that the surface bundlesM(F ′, f ′) andM(F, f ) have the same first Betti numbers. Mathematics Subject Classification (2000) Pseudo-Anosov extension · Degree-one maps ·Hyperbolic surface bundles
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تاریخ انتشار 2007