Slim unicorns and uniform hyperbolicity for arc graphs and curve graphs

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 close...

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Bibliographic Details
Main Authors Hensel, Sebastian, Przytycki, Piotr, Webb, Richard C. H
Format Journal Article
LanguageEnglish
Published 23.01.2013
Subjects
Mathematics - Geometric Topology
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Summary: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.
DOI:10.48550/arxiv.1301.5577