Cyclic Homology in Non-Commutative Geometry (Volume 121)

Cuntz, Joachim

ISBN 10: 3540404694 / ISBN 13: 9783540404699

Published by Springer, 2004

About this Item

Volume 121. This is an ex-library book and may have the usual library/used-book markings inside.This book has hardback covers. In good all round condition. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,450grams, ISBN:9783540404699.

Seller Inventory # 5569037

Bibliographic Details

• Title: Cyclic Homology in Non-Commutative Geometry (Volume 121)
• Publisher: Springer
• Publication Date: 2004
• Language: English
• ISBN 10: 3540404694
• ISBN 13: 9783540404699
• Binding: Hardcover
• Condition: Good
• Weight: 450 grams
• Seller catalogs:
  • Mathematics

About this title

Synopsis

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.

Review

From the reviews:

"This volume of the ‘Encyclopedia of Mathematical Sciences’ is a very important and useful contribution to the literature on cyclic homology and noncommutative geometry. ... This book contains three expository articles, covering very important recent results." (Alexander Gorokhovsky, Mathematical Reviews, 2005 k)