The study identifies conditions preventing hyperbolic spaces from being quasi-isometric to curve complexes, indicating theoretical implications.
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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Aramayona et al. (2026) studied this question.
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