A characterization of the Dirac Dual Dirac Method

Let G be a discrete, torsion free group with a finite dimensional classifying space BG. We show that the existence of a gamma-element for such G is a metric, that is, coarse, invariant of G. We also obtain results for groups with torsion. The method of proof involves showing that a group G possesses a gamma-element if and only if a certain coarse (co)-assembly map is an isomorphism.