Michael Puschnigg

Asymptotic Cyclic Cohomology

• Broschiertes Buch

Produktbeschreibung

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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Produktdetails

• Lecture Notes in Mathematics 1642
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-61986-4
• 1996.
• Seitenzahl: 268
• Erscheinungstermin: 16. Dezember 1996
• Englisch
• Abmessung: 235mm x 155mm x 15mm
• Gewicht: 412g
• ISBN-13: 9783540619864
• ISBN-10: 3540619860
• Artikelnr.: 23402871

Inhaltsangabe

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.