Cyclic Homology in Non-Commutative Geometry

Joachim Cuntz

ISBN 10: 3642073379 / ISBN 13: 9783642073373

Published by Springer Berlin Heidelberg, 2011

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783642073373

Bibliographic Details

• Title: Cyclic Homology in Non-Commutative Geometry
• Publisher: Springer Berlin Heidelberg
• Publication Date: 2011
• Language: English
• ISBN 10: 3642073379
• ISBN 13: 9783642073373
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 9D millimeters 235 millimeters width by 155 millimeters height by 9 millimeters depth
• Weight: 248 grams

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)