Vol. 296, No. 2, 2018

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Hyperbolic manifolds containing high topological index surfaces

Marion Campisi and Matt Rathbun

Vol. 296 (2018), No. 2, 305–319
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
Authors
 Marion Campisi Mathematics and Statistics Department San José State University San José, CA United States Matt Rathbun Department of Mathematics California State University, Fullerton Fullerton, CA United States