Geodesic
Thin buildings
Dymara, Jan1
1 Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Geometry & topology, Tome 10 (2006) no. 2, pp. 667-694.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/gt.2006.10.667
Keywords: building, $L^2$-cohomology, Hecke algebra

Dymara, Jan 1

1 Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland 
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Dymara, Jan. Thin buildings. Geometry & topology, Tome 10 (2006) no. 2, pp. 667-694. doi : 10.2140/gt.2006.10.667. http://geodesic.mathdoc.fr/articles/10.2140/gt.2006.10.667/

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