Hyperbolic spaces not quasi-isometric to curve complexes

Javier Aramayona; Hugo Parlier; Richard Webb

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arXiv · 2507.08086

Hyperbolic spaces not quasi-isometric to curve complexes

Javier Aramayona·Hugo Parlier·Richard Webb

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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.

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BibTeX RIS

Javier Aramayona, Hugo Parlier, Richard Webb. 2025-07-10. Hyperbolic spaces not quasi-isometric to curve complexes. https://arxiv.org/abs/2507.08086

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