Hyperbolization of a pseudo-Anosov mapping torus
= Hyperbolization of a pseudo-Anosov mapping torus
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The interior of the mapping torus of a pseudo-Anosov homeomorphism of a compact surface with boundary admits a complete finite-volume hyperbolic metric. Periodic monodromy instead gives a Seifert fibered mapping torus, while reducible monodromy gives a manifold containing an essential torus.