Hyperbolic spaces not quasi-isometric to curve complexes
Geometric Topology
2025-07-14 v1 Group Theory
Metric Geometry
Abstract
We identify a condition that prevents a hyperbolic space from being quasi-isometric to the curve complex of any non-sporadic surface. Our result applies to several hyperbolic complexes, including arc complexes, disk complexes, non-separating curve complexes, (hyperbolic) pants complexes, and to free splitting complexes of free groups.
Cite
@article{arxiv.2507.08086,
title = {Hyperbolic spaces not quasi-isometric to curve complexes},
author = {Javier Aramayona and Hugo Parlier and Richard Webb},
journal= {arXiv preprint arXiv:2507.08086},
year = {2025}
}
Comments
8 pages