English

Slim unicorns and uniform hyperbolicity for arc graphs and curve graphs

Geometric Topology 2013-01-24 v1

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.

Keywords

Cite

@article{arxiv.1301.5577,
  title  = {Slim unicorns and uniform hyperbolicity for arc graphs and curve graphs},
  author = {Sebastian Hensel and Piotr Przytycki and Richard C. H. Webb},
  journal= {arXiv preprint arXiv:1301.5577},
  year   = {2013}
}

Comments

6 pages, 1 figure

R2 v1 2026-06-21T23:14:18.195Z