Arc and curve graphs for infinite-type surfaces
Geometric Topology
2015-11-11 v2
Abstract
We study arc graphs and curve graphs for surfaces of infinite topological type. First, we define an arc graph relative to a finite number of (isolated) punctures and prove that it is a connected, uniformly hyperbolic graph of infinite diameter; this extends a recent result of J. Bavard to a large class of punctured surfaces. Second, we study the subgraph of the curve graph spanned by those elements which intersect a fixed separating curve on the surface. We show that this graph has infinite diameter and geometric rank 3, and thus is not hyperbolic.
Keywords
Cite
@article{arxiv.1510.07805,
title = {Arc and curve graphs for infinite-type surfaces},
author = {Javier Aramayona and Ariadna Fossas and Hugo Parlier},
journal= {arXiv preprint arXiv:1510.07805},
year = {2015}
}
Comments
12 pages, 2 figures. Corrections made, a proof simplified, main results unchanged