Joachim Cuntz

(Author)

Cyclic Homology in Non-Commutative GeometryPaperback, 23 January 2011

Cyclic Homology in Non-Commutative Geometry
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Part of Series
Encyclopaedia of Mathematical Sciences
Print Length
137 pages
Language
English
Publisher
Springer
Date Published
23 Jan 2011
ISBN-10
3642073379
ISBN-13
9783642073373

Description

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.

Product Details

Authors:
Joachim CuntzGeorges SkandalisBoris Tsygan
Book Format:
Paperback
Country of Origin:
NL
Date Published:
23 January 2011
Dimensions:
23.39 x 15.6 x 0.84 cm
ISBN-10:
3642073379
ISBN-13:
9783642073373
Language:
English
Location:
Berlin, Heidelberg
Pages:
137
Publisher:
Weight:
222.26 gm

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