Uniform hyperbolicity of the graphs of nonseparating curves via bicorn\n curves

2017/07/26 by Alexander J. Rasmussen, Rasmussen, Alexander J. · 1 citation
Mathematics · Computer Science · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1707.08283

Abstract

We show that the graphs of nonseparating curves for oriented finite type\nsurfaces are uniformly hyperbolic. Our proof follows the proof of uniform\nhyperbolicity of the graphs of curves for closed surfaces due to\nPrzytycki-Sisto, while introducing new arguments using homology to certify that\ncertain curves are nonseparating. As demonstrated by Aramayona-Valdez, this\nproves also that the graph of nonseparating curves for any oriented infinite\ntype surface with finite positive genus is hyperbolic.\n

Cited by

• The bicorn curves on closed surfaces

Related

• Uniform hyperbolicity of nonseparating curve graphs of nonorientable surfaces
• Geometry of the graphs of nonseparating curves: covers and boundaries
• Uniform Hyperbolicity of the Graphs of Curves
• The (non)-relative hyperbolicity of the separating curve graph
• The bicorn curves on closed surfaces