Cyclic Homology in Non-Commutative Geometry (Encyclopaedia of Mathematical Sciences, 121, Band 121) - Hardcover

Cuntz, Joachim; Skandalis, Georges; Tsygan, Boris

Hardcover

ISBN 10: 3540404694 ISBN 13: 9783540404699

Verlag: Springer, 2003

Inhaltsangabe

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 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 first phase it was tried to treat this structure as well as possible within the traditional framework of homological algebra. The cyclic homology groups were computed in many examples and new important properties such as prod­ uct structures, excision for H-unital ideals, or connections with cyclic objects and simplicial topology, were established. An excellent account of the state of the theory after that phase is given in the book of Loday.

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Über die Autorin bzw. den Autor

Joachim Cuntz is a full Professor at the Westfälische Wilhelms-Universität in Münster, Germany. Siegfried Echterhoff is a full Professor at the Westfälische Wilhelms-Universität in Münster, Germany. Xin Li is a Senior Lecturer in Pure Mathematics at Queen Mary University of London, United Kingdom. Guoliang Yu is Powell Chair in Mathematics and Professor at the Texas A&M University, USA.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2003
• Sprache: Englisch
• ISBN 10: 3540404694
• ISBN 13: 9783540404699
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 150
• Kontakt zum Hersteller: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Deutschland