The geometry of the disk complex

2010/10/15 by Howard Masur, Masur, Howard, Saul Schleimer +1 · 8 citations
Mathematics · #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M50

paper · pdf · doi:10.48550/arxiv.1010.3174

73 pages

arxiv created 2010/10/15 · arxiv updated 2010/10/18

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.

Cited by

• The bicorn curves on closed surfaces
• Balanced curves, quasimorphisms, and the equator conjecture
• The metric Rips filtration, universal quasigeodesic cones, and hierarchically hyperbolic spaces
• The arc complex is not quasi-isometric to the sphere complex
• Compressed data structures for Heegaard splittings
• The infinite dimensional geometry of conjugation invariant generating sets
• Mapping class groups of Heegaard splittings of surface bundles
• Comparing h-genera, Bridge-1 genera and Heegaard genera of knots

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