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Asymptotic Cyclic Cohomology : Lecture Notes in Computer Science, - Michael Puschnigg

Asymptotic Cyclic Cohomology

Lecture Notes in Computer Science,

Paperback Published: 16th December 1996
ISBN: 9783540619864
Number Of Pages: 244

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The aim of cyclic cohomology theories is the approximation of K-theory by cohomology theories defined by natural chain complexes. The basic example is the approximation of topological K-theory by de Rham cohomology via the classical Chern character. A cyclic cohomology theory for operator algebras is developed in the book, based on Connes' work on noncommutative geometry. Asymptotic cyclic cohomology faithfully reflects the basic properties and features of operator K-theory. It thus becomes a natural target for a Chern character. The central result of the book is a general Grothendieck-Riemann-Roch theorem in noncommutative geometry with values in asymptotic cyclic homology. Besides this, the book contains numerous examples and calculations of asymptotic cyclic cohomology groups.

The asymptotic homotopy categoryp. 1
Algebraic de Rham complexesp. 19
Cyclic cohomologyp. 27
Homotopy properties of X-complexesp. 40
The analytic X-complexp. 59
The asymptotic X-complexp. 97
Asymptotic cohomology of dense subalgebrasp. 118
Productsp. 127
Exact sequencesp. 158
KK-Theory and asymptotic cohomologyp. 182
Examplesp. 202
Index of Notationsp. 232
Index of Symbolsp. 235
Bibliographyp. 237
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540619864
ISBN-10: 3540619860
Series: Lecture Notes in Computer Science,
Audience: General
Format: Paperback
Language: English
Number Of Pages: 244
Published: 16th December 1996
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.42
Weight (kg): 0.38