Hyperbolic manifolds containing high topological index surfaces

Marion Campisi; Matt Rathbun

doi:10.2140/pjm.2018.296.305

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arXiv · 1706.00462

Hyperbolic manifolds containing high topological index surfaces

Marion Campisi·Matt Rathbun

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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 $n$.

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Marion Campisi, Matt Rathbun. 2017-06-01. Hyperbolic manifolds containing high topological index surfaces. https://doi.org/10.2140/pjm.2018.296.305

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