Abstract
Let be a building of uniform thickness . –Betti numbers of are reinterpreted as von-Neumann dimensions of weighted –cohomology of the underlying Coxeter group. The dimension is measured with the help of the Hecke algebra. The weight depends on the thickness . The weighted cohomology makes sense for all real positive values of , and is computed for small . If the Davis complex of the Coxeter group is a manifold, a version of Poincaré duality allows to deduce that the –cohomology of a building with large thickness is concentrated in the top dimension.
Citation
Jan Dymara. "Thin buildings." Geom. Topol. 10 (2) 667 - 694, 2006. https://doi.org/10.2140/gt.2006.10.667
Information