Encyclopaedia of Mathematical Sciences Operator Algebras and Non-Commutative Geometry

Cyclic Homology in Non-Commutative Geometry

Authors: Cuntz, Joachim, Skandalis, Georges, Tsygan, Boris

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About this book

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.

Reviews

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)


Table of contents (3 chapters)

Table of contents (3 chapters)

Buy this book

eBook 93,08 €
price for Spain (gross)
  • ISBN 978-3-662-06444-3
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-3-540-40469-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 114,39 €
price for Spain (gross)
  • ISBN 978-3-642-07337-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
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  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Cyclic Homology in Non-Commutative Geometry
Authors
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
121
Copyright
2004
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-06444-3
DOI
10.1007/978-3-662-06444-3
Hardcover ISBN
978-3-540-40469-9
Softcover ISBN
978-3-642-07337-3
Series ISSN
0938-0396
Edition Number
1
Number of Pages
XIII, 137
Topics