Cyclic Homology in Non-Commutative Geometry (Encyclopaedia of Mathematical Sciences)

Description:

This volume contains contributions by three authors and treats aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different and complementary points of view. The 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. On the other hand, 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.

subjects: Noncommutative differential geometry,  Homology theory,  Geometry,  Operator algebras,  Algebraic topology,  Operator theory,  Mathematics,  Mathematical and Computational Physics Theoretical