Asymptotic cyclic cohomology
著者
書誌事項
Asymptotic cyclic cohomology
（Lecture notes in mathematics, 1642）
Springer, c1996
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注記
Bibliography: p. [237]-238
Includes indexes
内容説明・目次
内容説明
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.
目次
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.
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