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.
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