Uniform Hyperbolicity of the Curve Graph

30 January 2013
David Hume; Robert Kropholler; Martin Palmer and Alessandro Sisto
<p><span style="font-size: x-small;"><span style="font-size: 10pt;">We will discuss (very) recent work by Hensel; Przytycki and Webb, who 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. </span></span></p>
  • Junior Topology and Group Theory Seminar