Rapaport's conjecture on knot like groups via Novikov's completions and Bieri-Strebel-Renz invariant
by Dr Dessislava Kochloukova
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.
For More Information: Lawrence Reeves email: L.Reeves@ms.unimelb.edu.au