Topological and Bivariant K-Theory
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Beschreibung
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.
Topological K-theory is one of the most important invariants for noncommutative algebras. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory. This book describes a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, it details other approaches to bivariant K-theories for operator algebras. The book studies a number of applications, including 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.
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
Autor*in
Joachim Cuntz
Themen in »Topological and Bivariant K-Theory«
Homotopy K-theory Thom isomorphism functional calculus topological invariants