Work

End‐periodic homeomorphisms and volumes of mapping tori

Year: 2023

Type: article

Abstract: Given 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.

Source: Journal of Topology

DOI: 10.1112/topo.12277

Authors: Elizabeth Field, Heejoung Kim, Christopher Leininger, Marissa Loving

Institutions: University of Utah, The Ohio State University, Rice University, University of Wisconsin–Madison

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,710

Funder: National Science Foundation