Quasiflats in CAT(0) complexes

Abstract

We show that if X is a piecewise Euclidean 2-complex with a cocompact isometry group, then every 2-quasiflat in X is at finite Hausdorff distance from a subset which is locally flat outside a compact set, and asymptotically conical.

References in corpus (2)

• Automorphisms of two-dimensional right-angled Artin groups
• Induced quasi-actions: a remark

Cited by in corpus (30)

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• Cubulated groups: thickness, relative hyperbolicity, and simplicial boundaries
• Quasi-isometric classification of right-angled Artin groups I: the finite out case
• Bowditch's JSJ tree and the quasi-isometry classification of certain Coxeter groups, with an appendix written jointly with Christopher Cashen
• Groups quasi-isometric to RAAG's
• Measure equivalence classification of transvection-free right-angled Artin groups
• The geometry of the curve graph of a right-angled Artin group
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• Quasi-Euclidean tilings over 2-dimensional Artin groups and their applications
• Embeddability and universal theory of partially commutative groups
• Boundary amenability and measure equivalence rigidity among two-dimensional Artin groups of hyperbolic type
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• Embeddability and quasi-isometric classification of partially commutative groups
• Cocompactly cubulated 2-dimensional Artin groups
• Quasi-isometry invariants of weakly special square complexes
• Dehn functions and finiteness properties of subgroups of perturbed right-angled Artin groups
• Divergence in right-angled Coxeter groups
• Subdivision rules for special cubulated groups
• Abstract commensurators of right-angled Artin groups and mapping class groups
• Indecomposable surface bundles over surfaces
• Quasi-isometric classification of some high dimensional right-angled Artin groups
• Measure equivalence classification of right-angled Artin groups: the finite $\mathrm{Out}$ classes
• The quasi-isometry invariance of the Coset Intersection Complex
• Finite subgraphs of an extension graph
• $\mathrm{CAT}(0)$ Extensions of Right-angled Coxeter Groups
• Right-angled Artin groups with non-path-connected boundary