Cyclic Homology (Grundlehren der mathematischen Wissenschaften, 301)

From the reviews: "This is a very interesting book containing material for a comprehensive study of the cyclid homological theory of algebras, cyclic sets and S1-spaces. Lie algebras and algebraic K-theory and an introduction to Connes'work and recent results on the Novikov conjecture. The book requires a knowledge of homological algebra and Lie algebra theory as well as basic technics coming from algebraic topology. The bibliographic comments at the end of each chapter offer good suggestions for further reading and research. The book can be strongly recommended to anybody interested in noncommutative geometry, contemporary algebraic topology and related topics." European Mathematical Society Newsletter In this second edition the authors have added a chapter 13 on MacLane (co)homology. Front Matter....Pages I-XIX Hochschild Homology....Pages 1-49 Cyclic Homology of Algebras....Pages 51-88 Smooth Algebras and Other Examples....Pages 89-114 Operations on Hochschild and Cyclic Homology....Pages 115-155 Variations on Cyclic Homology....Pages 157-199 The Cyclic Category, Tor and Ext Interpretation....Pages 201-225 Cyclic Spaces and S 1 -Equivariant Homology....Pages 227-256 Chern Character....Pages 257-280 Classical Invariant Theory....Pages 281-298 Homology of Lie Algebras of Matrices....Pages 299-340 Algebraic K -Theory....Pages 341-380 Non-commutative Differential Geometry....Pages 381-398 Mac Lane (co)homology....Pages 399-445 Back Matter....Pages 447-516 Introduction Notation and Terminology Hochschild Homology Cyclic Homology of Algebras Smooth Algebras and Other Examples Operations on Hochschild and Cyclic Homology Variations on Cyclic Homology The Cyclic Category, Tor and Ext Interpretation Cyclic Spaces and S1-Equivariant Homology Chern Character Classical Invariant Theory Homology of Lie Algebras of Matrices Algebraic K-Theory Non-Commutative Differential Geometry Appendices: Hopf Algebras Simplicial Homology of Discrete Groups and Small Categories Spectral Sequences Smooth Algebras References Symbols Index Mac Lane (co)homology.