Cyclic Homology

This book is a comprehensive study of cyclic homology theory. The first part deals with Hochschild and cyclic homology of associative algebras, their variations (periodic theory, dihedral theory) and the comparison with de Rham comology theory. The second part deals with cyclic sets, cyclic spaces, their relationships with S1-equivariant homology and the Chern character of Connes. The third part is devoted to the homology of the Lie algebra of matrices (the Loday-Quillen-Tsygan theorem) and its variations (namely non-commutative Lie homology). The fourth part is an account of algebraic K-theory and its relationship to cyclic homology. The last chapter is an overview of some applications to non-commutative differential geometry (foliations, Novikov conjecture, idempotent conjecture) as devised by Alain Connes. §Most of the results treated in this book have already appeared in research articles. However some are new (non-commutative Lie homology for instance) and many proofs are either more explicit or simpler than the existing ones. Though this book was thought of a basic reference for researchers, several part of it are accessible to graduate students, since the material is almost self contained. It also contains a comprehensive list of references on the subject.