Uniform hyperbolicity for curve graphs of non-orientable surfaces
Erika Kuno
TL;DR
This paper extends the understanding of hyperbolicity in curve and arc graphs from orientable to non-orientable surfaces, establishing specific hyperbolicity constants for these graphs.
Contribution
It proves that curve graphs of non-orientable surfaces are 17-hyperbolic and determines hyperbolicity constants for arc and arc-curve graphs.
Findings
Curve graphs of non-orientable surfaces are 17-hyperbolic.
Arc graphs of non-orientable surfaces are 7-hyperbolic.
Arc-curve graphs of non-orientable surfaces are 9-hyperbolic.
Abstract
Hensel-Przytycki-Webb proved that all curve graphs of orientable surfaces are 17-hyperbolic. In this paper, we show that curve graphs of non-orientable surfaces are 17-hyperbolic by applying Hensel-Przytycki-Webb's argument. We also show that arc graphs of non-orientable surfaces are 7-hyperbolic, and arc-curve graphs of (non-)orientable surfaces are 9-hyperbolic.
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Taxonomy
TopicsGeometric and Algebraic Topology · Geometric Analysis and Curvature Flows · Mathematical Dynamics and Fractals