End‐periodic homeomorphisms and volumes of mapping tori

Given an irreducible, end-periodic homeomorphism f : S → $f: \rightarrow S$ of a surface with finitely many ends, all accumulated by genus, the mapping torus, M $M_f$ , is interior compact, atoroidal 3-manifold ¯ $\overline{M}_f$ incompressible boundary. Our main result upper bound on infimal hyperbolic volume in terms translation length $f$ pants graph $S$ . This builds work Brock and Agol finite-type setting. We also construct broad class examples homeomorphisms use them to show that our asymptotically sharp.