Browsing by Author "Kropholler, Peter H."

Now showing 1 - 3 of 3
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    Group-Graded Rings Satisfying the Strong Rank Condition
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2019) Kropholler, Peter H.; Lorensen, Karl
    A ring R satisfies the strong rank condition (SRC) if, for every natural number n, the free R-submodules of Rⁿ all have rank ≤n. Let G be a group and R a ring strongly graded by G such that the base ring R₁ is a domain. Using an argument originated by Laurent Bartholdi for studying cellular automata, we prove that R satisfies SRC if and only if R₁ satisfies SRC and G is amenable. The special case of this result for group rings allows us to prove a characterization of amenability involving the group von Neumann algebra that was conjectured by Wolfgang Lück. In addition, we include two applications to the study of group rings and their modules.
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    Topological and Geometric Methods in Group Theory
    (Zürich : EMS Publ. House, 2006) Kropholler, Peter H.; Vogtmann, Karen
    The focus of this meeting was the use of topological and geometric methods to study infinite discrete groups. These methods are increasingly being supplemented by powerful new techniques from analysis. Key topics included group actions on CAT(0) and tree-like spaces, filling invariants, cohomology, K-theory and ℓ2 -cohomology, amenability and Kazhdan’s property (T), and deformation spaces, curve complexes and Teichmüller space.
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    Topologische Methoden in der Gruppentheorie
    (Oberwolfach-Walke : Mathematisches Forschungsinstitut Oberwolfach, 2001) Kropholler, Peter H.; Vogtmann, Karen
    [no abstract available]