End‐periodic homeomorphisms and volumes of mapping tori

Abstract

AbstractGiven an irreducible, end‐periodic homeomorphism of a surface with finitely many ends, all accumulated by genus, the mapping torus, , is the interior of a compact, irreducible, atoroidal 3‐manifold with incompressible boundary. Our main result is an upper bound on the infimal hyperbolic volume of in terms of the translation length of on the pants graph of . 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.