The L^2-cohomology of negatively curved Riemannian symmetric spaces

DOI10.5186/aasfm.1985.1012zbMath0586.57022OpenAlexW2322452168WikidataQ115159909 ScholiaQ115159909MaRDI QIDQ3711383

Armand Borel

Publication date: 1985

Published in: Annales Academiae Scientiarum Fennicae. Series A. I. Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5186/aasfm.1985.1012

zbMATH Keywords

unitary representationdiscrete series representationsinfinitesimal characterirreducible finite dimensional representation\(L^ 2\)-cohomology spacemaximal compact subgroup of a connected linear semisimple Lie groupRiemannian symmetric space with negative curvature

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Semisimple Lie groups and their representations (22E46) Differential geometry of symmetric spaces (53C35) Homology and cohomology of homogeneous spaces of Lie groups (57T15)

Related Items (18)

Poisson equation for differential forms on a symmetric space and applications ⋮ On the top-dimensional \(\ell^2\)-Betti numbers ⋮ \(L^p\)-cohomology in degree 1 of homogeneous spaces ⋮ The differential form spectrum of quaternionic hyperbolic spaces ⋮ Unnamed Item ⋮ Vanishing of \(L^{2}\)-Betti numbers and failure of acylindrical hyperbolicity of matrix groups over rings ⋮ Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices ⋮ Non-vanishing for group \(L^p\)-cohomology of solvable and semisimple Lie groups ⋮ Smith theory, \(L^2\)-cohomology, isometries of locally symmetric manifolds, and moduli spaces of curves ⋮ Harmonic analysis for differential forms on complex hyperbolic spaces ⋮ Quasi-isometric invariance of continuous group \(L^p\)-cohomology, and first applications to vanishings ⋮ Profinite invariants of arithmetic groups ⋮ Characters, \(L^2\)-Betti numbers and an equivariant approximation theorem ⋮ \(L^2\)-Betti numbers and Plancherel measure ⋮ The first \(L^2\)-Betti number of certain homogeneous spaces, including classifying spaces for variations of Hodge structures ⋮ \(L^{2}\)-invariants of nonuniform lattices in semisimple Lie groups ⋮ Profinite commensurability of $S$-arithmetic groups ⋮ \(L^2\) cohomology and parabolicity

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