Affiliation:
1. Department of Mathematics University of Utah Salt Lake City Utah USA
2. Department of Mathematics Ohio State University Columbus Ohio USA
3. Department of Mathematics Rice University Houston Texas USA
4. Department of Mathematics University of Wisconsin‐Madison Madison Wisconsin USA
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.
Funder
National Science Foundation
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