On the cuspidal cohomology of arithmetic subgroups of SL(2n) and the first Betti number of arithmetic 3-manifolds

DOI10.1215/S0012-7094-87-05525-6zbMath0648.22007OpenAlexW1572735334MaRDI QIDQ1105057

Laurent Clozel

Publication date: 1987

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-87-05525-6

zbMATH Keywords

number fieldfinite coveringcuspidal cohomologydeep arithmetic subgroups

Mathematics Subject Classification ID

Homology and cohomology of Lie groups (57T10) Discrete subgroups of Lie groups (22E40) Linear algebraic groups over global fields and their integers (20G30) Cohomology theory for linear algebraic groups (20G10)

Related Items (14)

Surface subgroups of Kleinian groups with torsion ⋮ Totally geodesic surfaces in hyperbolic 3-manifolds ⋮ Non-minimal modular symbols for GL(n) ⋮ On Cuspidal Cohomology of Arithmetic Groups and Cyclic Base Change ⋮ Non-simple geodesics in hyperbolic 3-manifolds ⋮ On the cohomology of trialitary hyperbolic varieties of dimension 7 ⋮ Nonvanishing square-integrable automorphic cohomology classes: the case \(\operatorname{GL}(2)\) over a central division algebra ⋮ Some consequences of Arthur's work on the spectrum and topology of hyperbolic varieties ⋮ Représentations galoisiennes associées aux représentations automorphes autoduales de \(GL(n)\). (Galois representations associated with self-dual automorphic representations of \(GL(n)\)) ⋮ Geometric cycles, arithmetic groups and their cohomology ⋮ Automorphic representations and Lefschetz numbers ⋮ Automorphic forms and rational homology 3-spheres ⋮ Vanishing of the cuspidal cohomology of congruence subgroups of \(\text{GL}_ n(\mathbb{Z})\) ⋮ A construction of residues of Eisenstein series and related square-integrable classes in the cohomology of arithmetic groups of low \(k\)-rank

Cites Work

• Regularization theorems in Lie algebra cohomology. Applications
• On liftings and cusp cohomology of arithmetic groups
• Relative Lie algebra cohomology and unitary representations of complex Lie groups
• Unitary representations of Gl(n,R) with non-trivial (g,K)-cohomology
• Automorphic forms on GL (2)
• Solvable and Nonsolvable CM-Fields
• On Euler Products and the Classification of Automorphic Representations I
• Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120)
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