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.
Includes bibliographical references (p. -507) and index.
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
K-Theory In this 2nd edition a new chapter 13 on MacLane (co)homology is added. It is compared with a variant of algebraic K-theory called stable K-theory. It turns out that these two theories are isomorphic. The main tool for this comparison is a third t
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