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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
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.