The property that the polynomial cohomology with coefficients of a finitely generated discrete group is canonically isomor-phic to the group cohomology is called the (weak) isocohomological property for the group. In the case when a group is of type HF ∞ , i.e. that has a classifying space with the homotopy type of a cellular complex with finitely many… (More)
We survey the cyclic cohomology associated with various algebras related to discrete groups. We then discuss the motivation and techniques of the cyclic theory approach to various problems in algebra and analysis.