Relatively geometric actions of Kähler groups on CAT(0) cube complexes

DOI10.2140/AGT.2024.24.4127MaRDI QIDQ6657467

Kejia Zhu, Daniel Groves, Corey Bregman

Publication date: 6 January 2025

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

zbMATH Keywords

relatively hyperbolic groupCAT(0) cube complextoroidal compactificationKähler groupcomplex hyperbolic latticecubulated group

Mathematics Subject Classification ID

Geometric group theory (20F65) Discrete subgroups of Lie groups (22E40) Compact Kähler manifolds: generalizations, classification (32J27) Algebraic topology of manifolds (57N65) Compactification of analytic spaces (32J05)

Cites Work

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• The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning).
• Ubiquitous quasi-Fuchsian surfaces in cusped hyperbolic 3-manifolds
• Peripheral fillings of relatively hyperbolic groups.
• Dehn filling in relatively hyperbolic groups.
• Thick metric spaces, relative hyperbolicity, and quasi-isometric rigidity.
• Groups acting on \(\text{CAT}(0)\) cube complexes
• Harmonic maps into singular spaces and \(p\)-adic superrigidity for lattices in groups of rank one
• Cusp closing in rank one symmetric spaces
• Cubulable Kähler groups
• Criterion for Cannon's conjecture.
• Hyperbolic groups with planar boundaries
• A boundary criterion for cubulation.
• Examples of Fundamental Groups of Compact Kähler Manifolds
• Rank one lattices whose parabolic isometries have no rotational part
• Dehn fillings and elementary splittings
• The Structure of Groups with a Quasiconvex Hierarchy
• Relative cubulations and groups with a 2-sphere boundary
• Hyperplane sections in arithmetic hyperbolic manifolds
• Relatively hyperbolic groups
• Hyperbolic groups acting improperly
• Isometries of CAT(0) cube complexes are semi-simple
• Relatively geometric actions on CAT$\operatorname{CAT}$(0) cube complexes
• Separation and relative quasiconvexity criteria for relatively geometric actions

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