springer.com Joachim Cuntz, Georges Skandalis, Boris Tsygan Cyclic Homology in Non- Commutative Geometry Series: Encyclopaedia of Mathematical Sciences Operator algebras and non-commutative geometry is one of the most exciting and active research areas in mathematics Contributing authors are top experts in the field, making this subseries unique Comprehensive coverage of the field Cyclic homology was introduced in the early eighties independently by Connes and Tsygan. They came from different directions. Connes wanted to associate homological invariants to K- homology classes and to describe the index pair• ing with K-theory in that way, while Tsygan was motivated by algebraic K-theory and Lie algebra cohomology. At the same time Karoubi had done work on characteristic classes that led him to study related structures, without however arriving at cyclic homology properly speaking. Many of the principal properties of 2004, XIII, 137 p. cyclic homology were already developed in the fundamental article of Connes and in the long paper by Feigin-Tsygan. In the sequel, cyclic homology was recognized quickly by many specialists as a new intriguing structure in homological algebra, with unusual features. In a Printed book first phase it was tried to treat this structure as well as possible within the traditional Hardcover framework of homological algebra. The cyclic homology groups were computed in many 109,99 € | £99.99 | $139.99 examples and new important properties such as prod• uct structures, excision for H-unital [1]117,69 € (D) | 120,99 € (A) | CHF ideals, or connections with cyclic objects and simplicial topology, were established. An excellent 130,00 account of the state of the theory after that phase is given in the book of Loday. Softcover 109,99 € | £99.99 | $139.99 [1]117,69 € (D) | 120,99 € (A) | CHF 130,00 eBook 93,08 € | £79.50 | $109.00 [2]93,08 € (D) | 93,08 € (A) | CHF 104,00 Available from your library or springer.com/shop MyCopy [3] Printed eBook for just € | $ 24.99 springer.com/mycopy Order online at springer.com / or for the Americas call (toll free) 1-800-SPRINGER / or email us at: [email protected]. / For outside the Americas call +49 (0) 6221-345-4301 / or email us at: [email protected]. The first € price and the £ and $ price are net prices, subject to local VAT. Prices indicated with [1] include VAT for books; the €(D) includes 7% for Germany, the €(A) includes 10% for Austria. Prices indicated with [2] include VAT for electronic products; 19% for Germany, 20% for Austria. All prices exclusive of carriage charges. Prices and other details are subject to change without notice. All errors and omissions excepted. [3] No discount for MyCopy. Part of .