Slim unicorns and uniform hyperbolicity for arc graphs and curve graphs

Sebastian Hensel; Piotr Przytycki; Richard C. H. Webb

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arXiv · 1301.5577

Slim unicorns and uniform hyperbolicity for arc graphs and curve graphs

Sebastian Hensel·Piotr Przytycki·Richard C. H. Webb

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Abstract

We describe unicorn paths in the arc graph and show that they form 1-slim triangles and are invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Considering the same paths in the arc and curve graph, this also shows that all curve graphs are 17-hyperbolic, including closed surfaces.

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BibTeX RIS

Sebastian Hensel, Piotr Przytycki, Richard C. H. Webb. 2013-01-23. Slim unicorns and uniform hyperbolicity for arc graphs and curve graphs. https://arxiv.org/abs/1301.5577

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