Volume 10, issue 2 (2006)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Thin buildings

Jan Dymara

Geometry & Topology 10 (2006) 667–694

arXiv: math.GT/0601005

Abstract

Let X be a building of uniform thickness q + 1. L2–Betti numbers of X are reinterpreted as von-Neumann dimensions of weighted L2–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 Poincaré duality allows to deduce that the L2–cohomology of a building with large thickness is concentrated in the top dimension.

Keywords
building, $L^2$-cohomology, Hecke algebra
Mathematical Subject Classification 2000
Primary: 20F55
Secondary: 20C08, 58J22, 20E42
References
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Publication
Received: 6 January 2006
Accepted: 30 April 2006
Published: 24 May 2006
Proposed: Wolfgang Lück
Seconded: Martin Bridson, Steve Ferry
Authors
Jan Dymara
Instytut Matematyczny
Uniwersytet Wrocławski
pl. Grunwaldzki 2/4
50-384 Wrocław
Poland