Cyclic Homology in Non-Commutative Geometry

This volume contains contributions by three authors and treats aspects of non-commutative geometry that are related to cyclic homology. The authors give complete accounts of cyclic theory from different and complementary points of view. These accounts cover in particular many advanced aspects of cyclic theory that have not been treated in book form until now. Cyclic theory is the natural setting for a variety of general index theorems. A survey of such index theorems (including the abstract index theorems of Connes-Moscovici and of Bressler-Nest-Tsygan) is given and the concepts and ideas involved in the proof of these theorems are explained. Moreover connections between topological (bivariant) K-theory and cyclic theory via generalized Chern-characters are discussed in detail. This includes an outline of a framework for bivariant K-theory on a category of locally convex algebras.