Analysis reveals volume of mapping tori is linked to translation length in end-periodic homeomorphisms, suggesting new insights.
We provide a lower bound on the volume of the compactified mapping torus of a strongly irreducible end‐periodic homeomorphism . This result, together with work of Field, Kim, Leininger, and Loving [J. Topol. 16 (2023), no. 1, 57–105], shows that the volume of is comparable to the translation length of on a connected component of the pants graph , extending work of Brock [Comm. Anal. Geom. 11 (2003), no. 5, 987–999] in the finite‐type setting on volumes of mapping tori of pseudo‐Anosov homeomorphisms.
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Field et al. (2025) studied this question.
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