A geometric criterion to be pseudo-Anosov

Richard P. Kent IV; Christopher J. Leininger

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arXiv · 1208.2494

A geometric criterion to be pseudo-Anosov

Richard P. Kent IV·Christopher J. Leininger

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Abstract

We establish a criterion for certain mapping classes of a surface homeomorphisms to be pseudo-Anosov in terms of the geometry of hyperbolic 3-manifolds and Gromov-hyperbolic surface group extensions. Specifically, any element of the fundamental group of a surface S gives rise to a mapping class on the punctured surface, and we show that such a class is pseudo-Anosov if its geodesic representative is "wide" in some hyperbolic 3-manifold homeomorphic to the trivial interval bundle over S.

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Richard P. Kent IV, Christopher J. Leininger. 2012-08-13. A geometric criterion to be pseudo-Anosov. https://arxiv.org/abs/1208.2494

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