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On ℓ2-homology of low dimensional buildings
Boros, Dan

2003, Doctor of Philosophy, Ohio State University, Mathematics.
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.
Michael Davis (Advisor)
77 p.

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Boros, D. (2003). On ℓ2-homology of low dimensional buildings. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Boros, Dan. "On ℓ2-homology of low dimensional buildings." Electronic Thesis or Dissertation. Ohio State University, 2003. OhioLINK Electronic Theses and Dissertations Center. 26 Sep 2017.

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Boros, Dan "On ℓ2-homology of low dimensional buildings." Electronic Thesis or Dissertation. Ohio State University, 2003. https://etd.ohiolink.edu/

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