Lectures on Cyclic Homology (Tata Institute of Fundamental Research Lectures on Mathemati)

The book is a basic introduction to the subject, divided into three parts. The first, Chapters 1 and 2, is background material on exact couples and Hochschild homology for the beginning reader. In Chapters 3, 4, 5 three definitions of cyclic homology are considered, its invariance under Morita equivalence, its relation to Lie algebra homology, and the Connes' B operator. The third part, Chapters 6 and 7, relates cyclichomology to differential forms and shows how the Chern character takes values in cyclic homology. Included is the classical Hochschild-Kostant-Rosenberg theorem relating differential forms to Hochschild homology. This introduction to cyclic homology is divided into three parts. The first part provides background material, part two considers three definitions of cyclic homology, and the third part relates cyclic homology to differential forms and shows how the Chern character takes values in cyclic homology.