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Birkhäuser - Birkhäuser Mathematics | Topological and Bivariant K-Theory

Topological and Bivariant K-Theory

Series: Oberwolfach Seminars, Vol. 36

Cuntz, Joachim, Rosenberg, Jonathan

2007, XI, 262 p.

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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.

Content Level » Research

Keywords » Homotopy - K-theory - Thom isomorphism - functional calculus - topological invariants

Related subjects » Birkhäuser Mathematics

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