On l^2-homology of low dimensional buildings

by Boros, Dan

Abstract (Summary)
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.
Bibliographical Information:


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

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