Cyclic Homology

Jean-Louis Loday (auth.)9780387533391, 0-387-53339-7

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 Mac Lane (co)homology.

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Table of contents :
Front Matter….Pages I-XVII
Hochschild Homology….Pages 1-49
Cyclic Homology of Algebras….Pages 50-87
Smooth Algebras and Other Examples….Pages 88-113
Operations on Hochschild and Cyclic Homology….Pages 114-154
Variations on Cyclic Homology….Pages 155-197
The Cyclic Category, Tor and Ext Interpretation….Pages 198-222
Cyclic Spaces and S 1 -Equivariant Homology….Pages 223-252
Chern Character….Pages 253-276
Classical Invariant Theory….Pages 277-294
Homology of Lie Algebras of Matrices….Pages 295-336
Algebraic K -Theory….Pages 337-376
Non-commutative Differential Geometry….Pages 377-394
Back Matter….Pages 395-454