English

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.

Keywords

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

R2 v1 2026-07-01T03:55:25.746Z