Maximal representations of uniform complex hyperbolic lattices

DOI10.4007/annals.2017.185.2.3zbMath1367.22004arXiv1506.07274OpenAlexW2962907228MaRDI QIDQ519651

Vincent Koziarz, Julien Maubon

Publication date: 5 April 2017

Published in: Annals of Mathematics. Second Series, Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.07274

zbMATH Keywords

Hermitian symmetric spacefoliationscomplex hyperbolic spacelocal rigidityMilnor-Wood inequalitycomplex hyperbolic cocompact latticesharmonic Higgs bundlesmaximal representationsToledo invariantsmooth varieties of general type

Mathematics Subject Classification ID

Vector bundles on surfaces and higher-dimensional varieties, and their moduli (14J60) Discrete subgroups of Lie groups (22E40) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Complex Lie groups, group actions on complex spaces (32M05)

Related Items (10)

Parametrizing Shimura subvarieties of \({\mathrm{A}_1}\) Shimura varieties and related geometric problems ⋮ Rigidity of maximal holomorphic representations of Kähler groups ⋮ Local rigidity of complex hyperbolic lattices in semisimple Lie groups ⋮ Maximal representations of cocompact complex hyperbolic lattices, a uniform approach ⋮ Arithmeticity, superrigidity and totally geodesic submanifolds of complex hyperbolic manifolds ⋮ Boundary maps and maximal representations on infinite-dimensional Hermitian symmetric spaces ⋮ Arakelov inequalities in higher dimensions ⋮ A Milnor-Wood inequality for complex hyperbolic lattices in quaternionic space ⋮ Algebraic hull of maximal measurable cocycles of surface groups into Hermitian Lie groups ⋮ Superrigidity of maximal measurable cocycles of complex hyperbolic lattices

Cites Work

• Local rigidity of discrete groups acting on complex hyperbolic space
• Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces
• Representations of complex hyperbolic lattices into rank 2 classical Lie groups of Hermitian type
• The complex-analyticity of harmonic maps and the strong rigidity of compact Kaehler manifolds
• Higgs bundles and local systems
• Lie groups and Teichmüller space
• On the rigidity of certain fundamental groups, arithmeticity of complex hyperbolic lattices, and the ``fake projective planes
• A negatively curved Kähler threefold not covered by the ball
• All regulators of flat bundles are torsion
• Factorization of semisimple discrete representations of Kähler groups
• Locally homogeneous complex manifolds
• Bounded differential forms, generalized Milnor-Wood inequality and an application to deformation rigidity
• The Self-Duality Equations on a Riemann Surface
• Constructing Variations of Hodge Structure Using Yang-Mills Theory and Applications to Uniformization
• Local Simple Connectedness of Resolutions of Log-Terminal Singularities

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