J. Cuntz, G. Skandalis, B. Tsygan

Cyclic Homology in Non-Commutative Geometry

• Gebundenes Buch

Produktbeschreibung

This volume contains contributions by three authors and treats aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different and complementary points of view. The connections between topological (bivariant) K-theory and cyclic theory via generalized Chern-characters are discussed in detail. This includes an outline of a framework for bivariant K-theory on a category of locally convex algebras. On the other hand, cyclic theory is the natural setting for a variety of general index theorems. A survey of such index theorems (including the abstract index theorems of Connes-Moscovici and of Bressler-Nest-Tsygan) is given and the concepts and ideas involved in the proof of these theorems are explained.

Produktdetails

• Encyclopaedia of Mathematical Sciences 121
• Verlag: SPRINGER, BERLIN
• Artikelnr. des Verlages: 978-3-540-40469-9
• 2004
• Seitenzahl: 156
• Erscheinungstermin: 17. November 2003
• Englisch
• Abmessung: 241mm x 160mm x 14mm
• Gewicht: 358g
• ISBN-13: 9783540404699
• ISBN-10: 3540404694
• Artikelnr.: 12229745

Inhaltsangabe

I. Cyclic Theory, Bivariant K-Theory and the Bivariant Chern-Connes Character by J. Cuntz: 1. Cyclic Theory; 2. Cyclic Theory for Locally Convex Algebras; 3. Bivariant K-Theory; 4. Infinite-Dimensional Cyclic Theories; A. Locally Convex Algebras; B. Standard Extensions.- II. Noncommutative Geometry, the Transverse Signature Operator, and Hopf Algebras (after A. Connes and H. Moscovici) by G. Skandalis: 1. Preliminaries; 2. The Local Index Formula; 3. The Diff-Invariant Signature Operator; 4. The 'Transverse' Hopf Algebra.- III. Cyclic Homology by B. Tsygan: 1. Introduction; 2. Hochschild and Cyclic Homology of Algebras; 3. The Cyclic Complex C^{lambda}_{bullet}; 4. Non-Commutative Differential Calculus; 5. Cyclic Objects; 6. Examples; 7. Index Theorems; 8. Riemann-Roch Theorem for D-Modules.

Rezensionen

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)