Cohomology of buildings and of their automorphism groups.

DOI10.1007/s00222-002-0242-yzbMath1140.20308OpenAlexW1978255231MaRDI QIDQ1401458

Publication date: 17 August 2003

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00222-002-0242-y

zbMATH Keywords

Coxeter groups unitary representations cohomological dimension locally compact groups Euclidean buildings products of trees Kazhdan property (T)Kazhdan groups a-T-menable groups cohomology of groups acting on buildings

Mathematics Subject Classification ID

Cohomology of groups (20J06) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Unitary representations of locally compact groups (22D10) Representations of Lie and linear algebraic groups over local fields (22E50) Groups with a (BN)-pair; buildings (20E42) Groups acting on trees (20E08) Means on groups, semigroups, etc.; amenable groups (43A07) Continuous cohomology of Lie groups (22E41)

Related Items (50)

Factor and normal subgroup theorems for lattices in products of groups ⋮ GOLOD–SHAFAREVICH GROUPS: A SURVEY ⋮ Buildings and Kac-Moody Groups ⋮ Cohomology of Coxeter groups with group ring coefficients. II. ⋮ Property $(T)$ for noncommutative universal lattices ⋮ $L^2$-Betti numbers of locally compact groups ⋮ Weighted $L^2$-cohomology of Coxeter groups. ⋮ Żuk’s criterion for Banach spaces and random groups ⋮ Tame automorphism groups of polynomial rings with property (T) and infinitely many alternating group quotients ⋮ Normal subgroups of SimpHAtic groups ⋮ Finitely presented simple groups and measure equivalence ⋮ Hyperbolic Kac-Moody Weyl groups, billiard tables and actions of lattices on buildings. ⋮ Groups graded by root systems and property ( T ) ⋮ High dimensional expanders and coset geometries ⋮ Infinite generation of non-cocompact lattices on right-angled buildings. ⋮ Property ($T$) for Kac-Moody groups over rings ⋮ Property (𝑇) for Groups Graded by Root Systems ⋮ Group algebra criteria for vanishing of cohomology ⋮ Cohomology computations for Artin groups, Bestvina-Brady groups, and graph products. ⋮ Lattices in complete rank 2 Kac-Moody groups. ⋮ On some pro-$p$ groups from infinite-dimensional Lie theory ⋮ Abstract simplicity of complete Kac-Moody groups over finite fields. ⋮ Expander graphs from Curtis-Tits groups. ⋮ Abstract involutions of algebraic groups and of Kac–Moody groups ⋮ On Garland's vanishing theorem for $\mathrm{SL}_n$ ⋮ Fixed-point theorems for groups acting on non-positively curved manifolds ⋮ Averaged projections, angles between groups and strengthening of Banach property (T) ⋮ Golod-Shafarevich groups with property $(T)$ and Kac-Moody groups. ⋮ Automorphism groups of simplicial complexes and rigidity for uniformly bounded representations ⋮ Non $p$-norm approximated groups ⋮ $L^2$-Betti numbers and Plancherel measure ⋮ A lattice in more than two Kac-Moody groups is arithmetic. ⋮ Nonassociative algebras and groups with property (T) ⋮ Hyperbolic configurations of roots and Hecke algebras ⋮ Superrigidity for irreducible lattices and geometric splitting ⋮ Poincaré inequalities and rigidity for actions on Banach spaces ⋮ Thin buildings. ⋮ $S$-arithmetic spinor groups with the same finite quotients and distinct $\ell^2$-cohomology ⋮ Kac-Moody groups and cosheaves on Davis building ⋮ On eigenvalues of $p$-adic curvature. ⋮ Simplicity and superrigidity of twin building lattices. ⋮ Product groups acting on manifolds ⋮ STABILITY, COHOMOLOGY VANISHING, AND NONAPPROXIMABLE GROUPS ⋮ $L^2$-cohomology of buildings with fundamental class ⋮ Cohomology of deformations ⋮ INFINITE DESCENDING CHAINS OF COCOMPACT LATTICES IN KAC–MOODY GROUPS ⋮ Arithmeticity vs. nonlinearity for irreducible lattices ⋮ Integrability of induction cocycles for Kac-Moody groups ⋮ Curvature criterion for vanishing of group cohomology ⋮ Vanishing of cohomology and property (T) for groups acting on weighted simplicial complexes

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