Slim unicorns and uniform hyperbolicity for arc graphs and curve graphs

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.

6 pages, 1 figure

References in corpus (1)

• Uniform Hyperbolicity of the Graphs of Curves

Cited by in corpus (3)

• A short proof of the bounded geodesic image theorem
• Combinatorial rigidity of arc complexes
• Efficient geodesics and an effective algorithm for distance in the complex of curves