Curve complexes are rigid

Abstract

Any quasi-isometry of the complex of curves is bounded distance from a simplicial automorphism. As a consequence, the quasi-isometry type of the curve complex determines the homeomorphism type of the surface.

20 pages, two figures, revised to reflect referee comments

References in corpus (3)

• Covers and the curve complex
• Geometry of the mapping class groups III: Quasi-isometric rigidity
• Connectivity of the space of ending laminations

Cited by in corpus (13)

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• Hyperbolic graphs for free products, and the Gromov boundary of the graph of cyclic splittings
• The geometry of the curve graph of a right-angled Artin group
• A positive proportion of elements of mapping class groups is pseudo-Anosov
• Dehn quandles of groups and orientable surfaces
• Automorphisms of the disk complex
• Proper actions on finite products of quasi-trees
• Automorphisms of the k-curve graph
• High distance knots in closed 3-manifolds
• Characterizing covers via simple closed curves
• Automorphisms of some variants of fine graphs
• Large-scale geometry of the saddle connection graph
• Bridge numbers of knots in the page of an open book