THE EULER CLASS OF A POINCARÉ DUALITY GROUP

Abstract

AbstractUnder an extra hypothesis satisfied in every known case, we show that the Euler class of an orientable odd-dimensional Poincaré duality group over any ring has order at most two. We construct groups that are of type FL over the complex numbers but are not FL over the rationals. We construct group algebras over fields for which $K_0$ contains torsion, and construct non-free stably free modules for the group algebras of certain virtually free groups.AMS 2000 Mathematics subject classification: Primary 19A31. Secondary 16S34; 20J05; 55N15; 57P10