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On ℓ2-homology of low dimensional buildings

Boros, Dan
http://rave.ohiolink.edu/etdc/view?acc_num=osu1062707630

Abstract Details

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.
Mathematics
l^2-homology; right-angled buildings

Recommended Citations

Citations

  • Boros, D. (2003). On ℓ2-homology of low dimensional buildings [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1062707630

    APA Style (7th edition)

  • Boros, Dan. On ℓ2-homology of low dimensional buildings. 2003. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1062707630.

    MLA Style (8th edition)

  • Boros, Dan. "On ℓ2-homology of low dimensional buildings." Doctoral dissertation, Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=osu1062707630

    Chicago Manual of Style (17th edition)

osu1062707630
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© 2003, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.