Asymptotic cyclic cohomology
By: Michael Puschnigg.
Series: Lecture notes in mathematics ;; 1642; Lecture notes in mathematics (Springer-Verlag) ;; 1642.
Publisher: Springer
Published: 1996
Place of publication: Berlin; New York
Language: eng
Number of pages: 238
Subjects: Homology theory; K-theory; KK-theory; Index theory (Mathematics)
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.
Notes: Includes bibliographical references (p. [237]-238) and indexes.