The geometry of the disk complex

By H. Masur, Saul Schleimer. 2010

173 citations recorded by the source corpus.

We give a distance estimate for the disk complex. We use the distance estimate to prove that the disk complex 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ab1b9595ccec97c8f62b79212a60e5e42badb1a3

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces (2013, background): “dix B. Green metrics on word-hyperbolic groups [11, Corollary 1.2] Quasihyperbolic metrics of uniform domains in Banach spaces [88, Theorem 2.12] Arc graphs and curve graphs [41] and arc complexes [57, 47] of nitely punctured oriented surfaces Free splitting complexes [40, 47] and free factor comple”
Quasi-morphisms on surface diffeomorphism groups (2019, background): “en Sis closed we have C(S) = Cs(S). In general the natural inclusion of the non-separating curve graph NC(S) into C(S) is not a quasi-isometric embedding (in fact it is arbitrarily distorted, compare [MS13]). However if Sis a surface of genus at least two with at most one marked point then one can e”