Joachim Cuntz, Jonathan M. Rosenberg

Topological and Bivariant K-Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

Topological K-theory is one of the most important invariants for noncommutative algebras equipped with a suitable topology or bornology. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory.

We describe a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, we discuss other approaches to bivariant K-theories for operator algebras. As applications, we study K-theory of crossed products, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem.

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Produktdetails

• Verlag: Birkhäuser Basel
• Seitenzahl: 262
• Erscheinungstermin: 4. Oktober 2007
• Englisch
• ISBN-13: 9783764383992
• Artikelnr.: 44130957

Autorenporträt

Joachim Cuntz, Westfälische Wilhelms-Universität, Münster, Germany / Ralf Meyer, Georg-August-Universität, Göttingen, Germany / Jonathan M. Rosenberg, University of Maryland, College Park, MD, USA

Inhaltsangabe

The elementary algebra of K-theory.- Functional calculus and topological K-theory.- Homotopy invariance of stabilised algebraic K-theory.- Bott periodicity.- The K-theory of crossed products.- Towards bivariant K-theory: how to classify extensions.- Bivariant K-theory for bornological algebras.- A survey of bivariant K-theories.- Algebras of continuous trace, twisted K-theory.- Crossed products by ? and Connes' Thom Isomorphism.- Applications to physics.- Some connections with index theory.- Localisation of triangulated categories.