Cyclic Homology
Springer Berlin (Verlag)
978-3-540-63074-6 (ISBN)
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.
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.
1. Hochschild Homology.- 2. Cyclic Homology of Algebras.- 3. Smooth Algebras and Other Examples.- 4. Operations on Hochschild and Cyclic Homology.- 5. Variations on Cyclic Homology.- 6. The Cyclic Category, Tor and Ext Interpretation.- 7. Cyclic Spaces and Sl-Equivariant Homology.- 8. Chern Character.- 9. Classical Invariant Theory.- 10. Homology of Lie Algebras of Matrices.- 11. Algebraic K-Theory.- 12. Non-commutative Differential Geometry.- 13. Mac Lane (co)homology.- Appendices.- A. Hopf Algebras.- B. Simplicial.- C. Homology of Discrete Groups and Small Categories.- D. Spectral Sequences.- E. Smooth Algebras.- References.- References 1992-1996.- Symbols.
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 (in the last chapter) 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 co
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 (in the last chapter) 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 co
| Erscheint lt. Verlag | 12.11.1997 |
|---|---|
| Reihe/Serie | Grundlehren der mathematischen Wissenschaften |
| Zusatzinfo | XIX, 516 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 888 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Schlagworte | Algebra • Algebraic K-Theory • algebraic topology • Algebraische Topologie • commutative property • Geometry • Homological algebra • Homology • Homology Theory • Invariant • K-theory algebra Algebras • Lie Algebras • Non-commutative Differential Geometry • Ring (Mathematik) • Topology |
| ISBN-10 | 3-540-63074-0 / 3540630740 |
| ISBN-13 | 978-3-540-63074-6 / 9783540630746 |
| Zustand | Neuware |
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