Thin buildings
Copyright policy )Thin buildings
Let X be a building of uniform thickness q+1. L^2-Betti numbers of X are reinterpreted as von-Neumann dimensions of weighted L^2-cohomology of the underlying Coxeter group. The dimension is measured with the help of the Hecke algebra. The weight depends on the thickness q. The weighted cohomology makes sense for all real positive values of q, and is computed for small q. If the Davis complex of the Coxeter group is a manifold, a version of Poincare duality allows to deduce that the L^2-cohomology of a building with large thickness is concentrated in the top dimension.
This is the version published by Geometry & Topology on 24 May 2006
- University of Wrocław Poland
Poincaré duality, Hecke algebra, Exotic index theories on manifolds, Coxeter groups, Group Theory (math.GR), Hecke algebras and their representations, 20F55, 20C08, 20E42, 58J22, Mathematics - Geometric Topology, Reflection and Coxeter groups (group-theoretic aspects), building, FOS: Mathematics, 20E42, Cohomology of groups, Hecke algebras, 20C08, Geometric Topology (math.GT), 58J22, buildings, \(L^2\)-cohomology, Groups with a \(BN\)-pair; buildings, weighted cohomology, Davis complexes, $L^2$-cohomology, 20F55, Mathematics - Group Theory
Poincaré duality, Hecke algebra, Exotic index theories on manifolds, Coxeter groups, Group Theory (math.GR), Hecke algebras and their representations, 20F55, 20C08, 20E42, 58J22, Mathematics - Geometric Topology, Reflection and Coxeter groups (group-theoretic aspects), building, FOS: Mathematics, 20E42, Cohomology of groups, Hecke algebras, 20C08, Geometric Topology (math.GT), 58J22, buildings, \(L^2\)-cohomology, Groups with a \(BN\)-pair; buildings, weighted cohomology, Davis complexes, $L^2$-cohomology, 20F55, Mathematics - Group Theory
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