Asymptotic cyclic cohomology
Author(s)
Bibliographic Information
Asymptotic cyclic cohomology
（Lecture notes in mathematics, 1642）
Springer, c1996
Available at / 87 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||1642RM970121
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Note
Bibliography: p. [237]-238
Includes indexes
Description and Table of Contents
Description
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.
Table of Contents
The asymptotic homotopy category.- Algebraic de Rham complexes.- Cyclic cohomology.- Homotopy properties of X-complexes.- The analytic X-complex.- The asymptotic X-complex.- Asymptotic cyclic cohomology of dense subalgebras.- Products.- Exact sequences.- KK-theory and asymptotic cohomology.- Examples.
by "Nielsen BookData"
