Asymptotic Cyclic Cohomology

Asymptotic Cyclic Cohomology
Author :
Publisher : Springer
Total Pages : 262
Release :
ISBN-10 : 9783540495796
ISBN-13 : 3540495797
Rating : 4/5 (96 Downloads)

Book Synopsis Asymptotic Cyclic Cohomology by : Michael Puschnigg

Download or read book Asymptotic Cyclic Cohomology written by Michael Puschnigg and published by Springer. This book was released on 2006-11-14 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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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