Lectures on Cyclic Homology

This book is a basic introduction to cyclic homology, 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 and 5 three definitions of cyclic homology are considered, its variance under Morita equivalence, its relation to Lie algebra homology, and the Connes' B operator. The third part, chapters 6 and 7, relates cyclic homology 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.