Author
Boros, Dan

Year
2003

Advisor
Davis, Michael W.

Abstract
We study topological invariants related to the l²-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 l²-Euler characteristic with respect to G and compute l²-Betti numbers for a variety of 2-dimensional right-angled buildings. One of these formulas relates the l²-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.

Thesis
Boros.Dan.pdf