Cross ratios and cubulations of hyperbolic groups

DOI10.1007/s00208-021-02330-3OpenAlexW4205744764WikidataQ115609064 ScholiaQ115609064MaRDI QIDQ2089720

Elia Fioravanti, Jonas Beyrer

Publication date: 24 October 2022

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.08087

Mathematics Subject Classification ID

Hyperbolic groups and nonpositively curved groups (20F67)

Related Items

Coarse-median preserving automorphisms ⋮ Homotopy equivalent boundaries of cube complexes ⋮ Sublinearly Morse boundaries from the viewpoint of combinatorics ⋮ Cross‐ratios on CAT(0) cube complexes and marked length‐spectrum rigidity

Cites Work

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• The Poisson boundary of CAT(0) cube complex groups.
• Immersing almost geodesic surfaces in a closed hyperbolic three manifold
• Combinatorial and group-theoretic compactifications of buildings
• Marked length rigidity for symmetric spaces
• Rank rigidity for CAT(0) cube complexes.
• Cubulating hyperbolic free-by-cyclic groups: the irreducible case
• Le spectre marqué des longueurs des surfaces à courbure négative. (The spectrum marked by lengths of surfaces with negative curvature)
• Rigidity for surfaces of non-positive curvature
• Cross ratios, surface groups, \(\text{PSL}(n,\mathbb R)\) and diffeomorphisms of the circle
• Kazhdan and Haagerup properties from the median viewpoint.
• Property \(A\) and \(\text{CAT}(0)\) cube complexes.
• The geometry of Teichmüller space via geodesic currents
• The marked length-spectrum of a surface of nonpositive curvature
• Cocycles, symplectic structures and intersection
• Hyperbolic buildings, conformal dimension and Mostow rigidity
• Codimension-1 subgroups and splittings of groups
• Groups acting on \(\text{CAT}(0)\) cube complexes
• Random walks and boundaries of CAT(0) cubical complexes
• Characterizations of Morse quasi-geodesics via superlinear divergence and sublinear contraction
• Morse boundaries of proper geodesic metric spaces
• Trees and ultrametric Möbius structures
• Cubulating spaces with walls.
• Cubulating small cancellation groups.
• A combination theorem for special cube complexes.
• Combinatorial modulus, the combinatorial Loewner property, and Coxeter groups.
• Contracting isometries of CAT(0) cube complexes and acylindrical hyperbolicity of diagram groups
• CAT(0) cube complexes are determined by their boundary cross ratio
• On hierarchical hyperbolicity of cubical groups
• Roller boundaries for median spaces and algebras
• Hyperbolicities in CAT(0) cube complexes
• Panel collapse and its applications
• Superrigidity of actions on finite rank median spaces
• Cubulable Kähler groups
• Cubulating hyperbolic free-by-cyclic groups: the general case
• Some applications of \(\ell_p\)-cohomology to boundaries of Gromov hyperbolic spaces
• Sur la géométrie symplectique de l'espace des géodésiques d'une variété à courbure négative. (On the symplectic geometry of the space of geodesics of a manifold with negative curvature)
• Special cube complexes
• Anosov flows, surface groups and curves in projective space
• Quasi-isometric rigidity of Fuchsian buildings
• The median class and superrigidity of actions on CAT(0) cube complexes
• A boundary criterion for cubulation
• Cubulating random groups at density less than $1/6$
• Greenberg's Theorem for Quasiconvex Subgroups of Word Hyperbolic Groups
• The Furstenberg–Poisson boundary and CAT(0) cube complexes
• FROM WALL SPACES TO CAT(0) CUBE COMPLEXES
• Manifolds with non-positive curvature
• Cocycles, Hausdorff measures and cross ratios
• Widths of Subgroups
• Coxeter Groups act on CAT(0) cube complexes
• Ends of Group Pairs and Non-Positively Curved Cube Complexes
• Un Groupe Hyperbolique Est Déterminé Par Son Bord
• A metrizable topology on the contracting boundary of a group
• Contracting boundaries of CAT(0) spaces
• Automorphisms of graph products of groups from a geometric perspective
• Hyperplane sections in arithmetic hyperbolic manifolds