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Roman Sauer

  1. The limit of F_p-Betti numbers of a tower of finite covers with amenable fundamental groups.

    Втр, 03/02/2010 - 16:01 — SomNambul
    Authors: Roman Sauer, Wolfgang Lueck, Peter Linnell
    Subjects: K-Theory and Homology
    Abstract

    We prove an analogue of the Approximation Theorem of L^2-Betti numbers by
    Betti numbers for arbitrary coefficient fields and virtually torsionfree
    amenable groups. The limit of Betti numbers is identified as the dimension of
    some module over the Ore localization of the group ring.

  2. Finiteness obstructions and Euler characteristics of categories.

    Втр, 08/25/2009 - 22:41 — SomNambul
    Authors: Wolfgang Lück, Thomas M. Fiore, Roman Sauer
    Subjects: Algebraic Topology
    Abstract

    We introduce notions of finiteness obstruction, Euler characteristic,
    L^2-Euler characteristic, and M\"obius inversion for wide classes of
    categories. The finiteness obstruction of a category \Gamma of type (FP) is a
    class in the projective class group K_0(R\Gamma); the Euler characteristic and
    L^2-Euler characteristic are respectively its R\Gamma-rank and L^2-rank. We
    also extend the second author's K-theoretic M\"obius inversion from finite
    categories to quasi-finite categories.

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