Morse functions to graphs and topological complexity for hyperbolic 3-manifolds

Diane Hoffoss; Joseph Maher

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arXiv · 1708.04140

Morse functions to graphs and topological complexity for hyperbolic 3-manifolds

Diane Hoffoss·Joseph Maher

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Abstract

Scharlemann and Thompson define the width of a 3-manifold M as a notion of complexity based on the topology of M. Their original definition had the property that the adjacency relation on handles gave a linear order on handles, but here we consider a more general definition due to Saito, Scharlemann and Schultens, in which the adjacency relation on handles may give an arbitrary graph. We show that for compact hyperbolic 3-manifolds, this is linearly related to a notion of metric complexity, based on the areas of level sets of Morse functions to graphs, which we call Gromov area.

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BibTeX RIS

Diane Hoffoss, Joseph Maher. 2017-08-11. Morse functions to graphs and topological complexity for hyperbolic 3-manifolds. https://arxiv.org/abs/1708.04140

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