A lower bound on volumes of end-periodic mapping tori

Elizabeth Field; Autumn Kent; Christopher Leininger; Marissa Loving

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arXiv · 2306.03279

A lower bound on volumes of end-periodic mapping tori

Elizabeth Field·Autumn Kent·Christopher Leininger·Marissa Loving

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Abstract

We provide a lower bound on the volume of the compactified mapping torus of a strongly irreducible end-periodic homeomorphism f. This result, together with work of Field, Kim, Leininger, and Loving, shows that the volume of the compactified mapping torus of f is comparable to the translation length of f on a connected component of the pants graph, extending work of Brock in the finite-type setting on volumes of mapping tori of pseudo-Anosov homeomorphisms.

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Elizabeth Field, Autumn Kent, Christopher Leininger, Marissa Loving. 2023-06-05. A lower bound on volumes of end-periodic mapping tori. https://arxiv.org/abs/2306.03279

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