Characteristic classes and representations of discrete subgroups of Lie groups

DOI10.1090/S0273-0979-1982-14974-6zbMath0493.57011OpenAlexW1977220192WikidataQ115282921 ScholiaQ115282921MaRDI QIDQ3956100

William M. Goldman

Publication date: 1982

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-1982-14974-6

zbMATH Keywords

Teichmüller spaceEuler numberspace of representationsEuler classbounded cohomologyMostow rigidityfoliated bundlevolume invariantcircle bundles over surfaces admitting flat structurescovering group of PSL(2,R)discrete subgroup of semisimple Lie groupinvariant closed differential form on symmetric spaceMargulis rigidityrepresentations of a countable group into a connected semisimple Lie group which are injective and whose image is a discrete cocompact subgroup

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Characteristic classes and numbers in differential topology (57R20) Discrete subgroups of Lie groups (22E40) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Foliations in differential topology; geometric theory (57R30) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) Connections (general theory) (53C05)

Related Items (17)

Cone 3-Manifolds ⋮ Bounded differential forms, generalized Milnor-Wood inequality and an application to deformation rigidity ⋮ Topological components of spaces of representations ⋮ A note on the integrality of volumes of representations ⋮ Convex Real Projective Structures on Closed Surfaces are Closed ⋮ The classification of real projective structures on compact surfaces ⋮ The geometry of synchronization problems and learning group actions ⋮ Volume invariant and maximal representations of discrete subgroups of Lie groups ⋮ Integrality of volumes of representations ⋮ Quantization of \(SL(2,\mathbb{R}{})\) Chern-Simons theory ⋮ Volume of representations and mapping degree ⋮ Maximal volume representations are Fuchsian ⋮ Local rigidity of discrete groups acting on complex hyperbolic space ⋮ Volume and symplectic structure for \(\ell\)-adic local systems ⋮ The median class and superrigidity of actions on CAT(0) cube complexes ⋮ Volumes in Seifert space ⋮ The symplectic nature of fundamental groups of surfaces

Cites Work

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• Elementary structure of real algebraic varieties
• Volume and bounded cohomology
• Simplices of maximal volume in hyperbolic n-space
• Foliated bundles, invariant measures and flat manifolds
• A generalization of Milnor's inequality concerning affine foliations and affine manifolds
• On discrete subgroups of Lie groups. I, II
• On the existence of a connection with curvature zero
• Topological properties of some spaces of stable bundles
• Bundles with totally disconnected structure group
• Ergodic theory, group representations, and rigidity
• Flat Bundles with Solvable Holonomy. II. Obstruction Theory
• Discrete groups of motions of manifolds of nonpositive curvature

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