Hyperbolic manifolds containing high topological index surfaces

Marion Campisi and Matt Rathbun

Vol. 296 (2018), No. 2, 305–319

DOI: 10.2140/pjm.2018.296.305

Abstract

If a graph is in bridge position in a 3-manifold so that the graph complement is irreducible and boundary-irreducible, we generalize a result of Bachman and Schleimer to prove that the complexity of a surface properly embedded in the complement of the graph bounds the graph distance of the bridge surface. We use this result to construct, for any natural number $n$, a hyperbolic manifold containing a surface of topological index $n$.

Keywords

topological index, topologically minimal, hyperbolic, bridge position, distance, bridge distance, graph

Mathematical Subject Classification 2010

Primary: 55P15, 57M20, 57M27

Secondary: 57M10, 57M15

Milestones

Received: 16 June 2017

Revised: 22 February 2018

Accepted: 4 April 2018

Published: 16 July 2018