Browsing by Author "Field, Elizabeth"

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    End-periodic homeomorphisms and volumes of mapping tori
    (Wiley, 2023) Field, Elizabeth; Kim, Heejoung; Leininger, Christopher; Loving, Marissa; Mathematics
    Given an irreducible, end-periodic homeomorphism f:S→S$f: S \rightarrow S$ of a surface with finitely many ends, all accumulated by genus, the mapping torus, Mf$M_f$, is the interior of a compact, irreducible, atoroidal 3-manifold M¯f$øverlineM_f$ with incompressible boundary. Our main result is an upper bound on the infimal hyperbolic volume of M¯f$øverlineM_f$ in terms of the translation length of f$f$ on the pants graph of S$S$. This builds on work of Brock and Agol in the finite-type setting. We also construct a broad class of examples of irreducible, end-periodic homeomorphisms and use them to show that our bound is asymptotically sharp.