Homotopy equivalent boundaries of cube complexes

DOI10.1007/s10711-023-00877-warXiv2303.06932OpenAlexW4391281602WikidataQ129149091 ScholiaQ129149091MaRDI QIDQ6120825

David Futer, Talia Fernós, Mark F. Hagen

Publication date: 21 February 2024

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.06932

zbMATH Keywords

CAT(0) cube complexnerve theoremTits boundaryroller boundary

Mathematics Subject Classification ID

Geometric group theory (20F65) Metric geometry (51F99)

Cites Work

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• Some properties of median metric spaces
• Ping pong on CAT(0) cube complexes
• The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning).
• The Poisson boundary of CAT(0) cube complex groups.
• Cell-like equivalences and boundaries of \(CAT(0)\) groups
• Rank rigidity for CAT(0) cube complexes.
• Higher rank hyperbolicity
• On equivariant homeomorphisms of boundaries of CAT(0) groups and Coxeter groups
• Examples of non-rigid \(\text{CAT}(0)\) groups from the category of knot groups.
• Property \(A\) and \(\text{CAT}(0)\) cube complexes.
• Homotopy type of posets and lattice complementation
• Boundaries of \(\text{CAT}(0)\) groups of the form \(\Gamma=G\times H\)
• The geometry of cube complexes and the complexity of their fundamental groups
• Random walks and boundaries of CAT(0) cubical complexes
• Corrigendum to: ``The simplicial boundary of a CAT(0) cube complex
• Cocompact CAT(0) spaces are almost geodesically complete
• The geodesic flow of a nonpositively curved graph manifold.
• Cubulating spaces with walls.
• Local homology properties of boundaries of groups
• The simplicial boundary of a CAT(0) cube complex
• Spaces with nonpositive curvature and their ideal boundaries
• Graphs of some CAT(0) complexes
• Contracting isometries of CAT(0) cube complexes and acylindrical hyperbolicity of diagram groups
• CAT(0) cube complexes are determined by their boundary cross ratio
• Cross ratios and cubulations of hyperbolic groups
• Large facing tuples and a strengthened sector lemma
• On hierarchical hyperbolicity of cubical groups
• Roller boundaries for median spaces and algebras
• The Tits alternative for finite rank median spaces
• Hierarchically hyperbolic spaces. I: Curve complexes for cubical groups
• Top-dimensional quasiflats in CAT(0) cube complexes
• Centers of convex subsets of buildings
• Cubulated groups: thickness, relative hyperbolicity, and simplicial boundaries
• Homology groups of relations
• At infinity of finite-dimensional CAT\((0)\) spaces
• The median class and superrigidity of actions on CAT(0) cube complexes
• The Tits boundary of a $\text {CAT}(0)$ 2-complex
• The Furstenberg–Poisson boundary and CAT(0) cube complexes
• FROM WALL SPACES TO CAT(0) CUBE COMPLEXES
• Geometric Group Theory
• A CAT(0) group with uncountably many distinct boundaries
• Ends of Group Pairs and Non-Positively Curved Cube Complexes
• Boundaries of nonpositively curved groups of the form G × ℤⁿ
• Deforming cubulations of hyperbolic groups
• The Structure of Groups with a Quasiconvex Hierarchy
• On the imbedding of systems of compacta in simplicial complexes
• The Paracompactness of the Weak Simplicial Complex
• Morse quasiflats. II
• Isometries of CAT(0) cube complexes are semi-simple

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