Pseudo-Anosov extensions and degree one maps between hyperbolic surface bundles |
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| Authors: | Michel Boileau Yi Ni Shicheng Wang |
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| Affiliation: | (1) Laboratoire émile Picard, Université Paul Sabatier, Toulouse Cedex 4, France;(2) Department of Mathematics, Princeton University, Princeton, NJ 08544, USA;(3) LMAM, Department of Mathematics, Peking University, Beijing, 100871, China |
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| Abstract: | 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 pseudo- Anosov 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 bundles M(F′,f′) and M(F,f) have the same first Betti numbers. Y. Ni is partially supported by a Centennial fellowship of the Graduate School at Princeton University. S.C. Wang is partially supported by MSTC |
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| Keywords: | Pseudo-Anosov extension Degree-one maps Hyperbolic surface bundles |
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