Uniform hyperbolicity of the graphs of nonseparating curves via bicorn curves

Rasmussen, Alexander

doi:10.1090/proc/14880

Uniform hyperbolicity of the graphs of nonseparating curves via bicorn curves
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by Alexander J. Rasmussen

Proc. Amer. Math. Soc. 148 (2020), 2345-2357

DOI: https://doi.org/10.1090/proc/14880

Published electronically: March 4, 2020

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Abstract:

We show that the graphs of nonseparating curves for oriented finite ctype surfaces are uniformly hyperbolic. Our proof follows the proof of uniform hyperbolicity of the graphs of curves for closed surfaces due to Przytycki–Sisto, while introducing new arguments using homology to certify that certain curves are nonseparating. As demonstrated by Aramayona–Valdez, this also proves that the graph of nonseparating curves for any oriented infinite type surface with finite positive genus is hyperbolic.

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