Asymptotic Cyclic Cohomology

By: Michael Puschnigg

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Paperback | 16 December 1996

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268 Pages

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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.

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The asymptotic homotopy category	p. 1
Algebraic de Rham complexes	p. 19
Cyclic cohomology	p. 27
Homotopy properties of X-complexes	p. 40
The analytic X-complex	p. 59
The asymptotic X-complex	p. 97
Asymptotic cohomology of dense subalgebras	p. 118
Products	p. 127
Exact sequences	p. 158
KK-Theory and asymptotic cohomology	p. 182
Examples	p. 202
Index of Notations	p. 232
Index of Symbols	p. 235
Bibliography	p. 237
Table of Contents provided by Blackwell. All Rights Reserved.

Asymptotic Cyclic Cohomology

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