The geometry of the disk complex
Howard Masur, Saul Schleimer
TL;DR
This paper establishes the Gromov hyperbolicity of the disk complex metric, provides a distance estimate, and introduces an algorithm to compute the Hempel distance of a Heegaard splitting with bounded error.
Contribution
It proves the hyperbolic nature of the disk complex metric and develops an algorithm for estimating Hempel distance with genus-dependent error bounds.
Findings
Disk complex metric is Gromov hyperbolic.
Provides a distance estimate for the disk complex.
Develops an algorithm to compute Hempel distance with error depending on genus.
Abstract
We give a distance estimate for the metric on the disk complex and show that it is Gromov hyperbolic. As another application of our techniques, we find an algorithm which computes the Hempel distance of a Heegaard splitting, up to an error depending only on the genus.
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Taxonomy
TopicsGeometric and Algebraic Topology · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology