JournalsjemsVol. 17, No. 4pp. 755–762

1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs

  • Sebastian Hensel

    University of Chicago, USA
  • Piotr Przytycki

    McGill University, Montreal, Canada
  • Richard C.H. Webb

    University College London, UK
1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs cover
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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.

Cite this article

Sebastian Hensel, Piotr Przytycki, Richard C.H. Webb, 1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs. J. Eur. Math. Soc. 17 (2015), no. 4, pp. 755–762

DOI 10.4171/JEMS/517