School Seminars and Colloquia

Rapaport's conjecture on knot like groups via Novikov's completions and Bieri-Strebel-Renz invariant

Geometry/Topology Seminar

by Dr Dessislava Kochloukova

Institution: University of Campinas, Brazil
Date: Mon 5th February 2007
Time: 3:15 PM
Location: Old Geology Theatre 2, The University of Melbourne

Abstract: We discuss applications of Bieri-Renz-Strebel homological invariants of groups and the Novikov rings associated to real characters of groups. In the case of a discrete character it was proved recently that the Novikov ring is von Neumann finite i.e., left inverse is a right inverse (the proof uses the existence of von Neumann dimension of finitely generated projective modules over the von Neumann algebra N(G)). As a corollary of the above results, some results due to J. Hillman and Stallings' characterization of groups of cohomological dimension 1 a conjecture due to E. Rapaport Strasser is proved :for every knot like group G with finitely generated commutator G', G' should be a free group.

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