On l^2-homology of low dimensional buildings
We study topological invariants related to the l^2-homology of low dimensional regular right-angled buildings. By definition, such buildings admit a chamber transitive automorphism group G. In this setting, we provide several formulas for the l^2-Euler characteristic with respect to G and compute l^2-Betti numbers for a variety of 2-dimensional right-angled buildings. One of these formulas relates the l^2-Euler characteristic to the h-polynomial of the nerve of the associated right-angled Coxeter group. Particularly interesting is the case where this nerve is a triangulation of a n-sphere. We prove that the h-polynomial associated with a flag triangulation of a n-sphere has real roots for n less or equal to 3.
School:The Ohio State University
School Location:USA - Ohio
Source Type:Master's Thesis
Keywords:l 2 homology right angled buildings
Date of Publication:01/01/2003