Asymptotic Cyclic Cohomology

1996
ISBN: 978-3-540-61986-4
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1642, 244 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 411 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Puschnigg, Michael

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

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.