Overview
- First available book on bivariant topological K-theory for algebras other than C*-algebras with complete proofs
- Several new results about bivariant K-theory for general algebras in this book did not even appear in journal publications before
- The exposition is accessible to graduate students
- Modern ideas from category theory are used to study bivariant K-theory
- Includes supplementary material: sn.pub/extras
Part of the book series: Oberwolfach Seminars (OWS, volume 36)
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Topological and Bivariant K-Theory
Authors: Joachim Cuntz, Ralf Meyer, Jonathan M. Rosenberg
Series Title: Oberwolfach Seminars
DOI: https://doi.org/10.1007/978-3-7643-8399-2
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Basel 2007
Softcover ISBN: 978-3-7643-8398-5Published: 19 July 2007
eBook ISBN: 978-3-7643-8399-2Published: 04 October 2007
Series ISSN: 1661-237X
Series E-ISSN: 2296-5041
Edition Number: 1
Number of Pages: XII, 262