UID:
almahu_9947921561302882
Format:
XXIV, 244 p.
,
online resource.
ISBN:
9783540495796
Series Statement:
Lecture Notes in Mathematics, 1642
Content:
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.
Note:
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.
In:
Springer eBooks
Additional Edition:
Printed edition: ISBN 9783540619864
Language:
English
Subjects:
Mathematics
URL:
http://dx.doi.org/10.1007/BFb0094458
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(Deutschlandweit zugänglich)
