Morse area and Scharlemann–Thompson width for hyperbolic 3-manifolds

Diane Hoffoss and Joseph Maher

Vol. 281 (2016), No. 1, 83–102

DOI: 10.2140/pjm.2016.281.83

Abstract

Scharlemann and Thompson define a numerical complexity for a $3$-manifold using handle decompositions of the manifold. We show that for compact hyperbolic $3$-manifolds, this is linearly related to a definition of metric complexity in terms of the areas of level sets of Morse functions.

Keywords

hyperbolic 3-manifold, Heegaard splitting, Morse function, Scharlemann–Thompson width

Mathematical Subject Classification 2010

Primary: 57M50

Secondary: 57N16

Milestones

Received: 30 March 2015

Revised: 23 July 2015

Accepted: 24 July 2015

Published: 9 February 2016