Separating Curve Complex of the Genus Two Surface is Hyperbolic
Harold Mark Sultan
TL;DR
This paper proves that the separating curve complex of a genus two surface is hyperbolic, providing a quasi-distance formula and confirming a conjecture by Schleimer using tools from Masur and Schleimer.
Contribution
It establishes the hyperbolicity of the separating curve complex for genus two surfaces and confirms Schleimer's conjecture with new quasi-distance formulas.
Findings
The separating curve complex is delta hyperbolic.
A quasi-distance formula for the complex is established.
The conjecture of Schleimer is affirmed.
Abstract
A proof that the separating curve complex of the closed genus two surface has a quasi-distance formula and is delta hyperbolic using tools of Masur and Schleimer. This answers in the affirmative a Conjecture of Schleimer.
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Taxonomy
TopicsGeometric and Algebraic Topology · Computational Geometry and Mesh Generation · Advanced Numerical Analysis Techniques