Topological and Bivariant K-Theory

  • Joachim Cuntz
  • Ralf Meyer
  • Jonathan M. Rosenberg

Part of the Oberwolfach Seminars book series (OWS, volume 36)

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.


Homotopy K-theory Thom isomorphism functional calculus topological invariants

Authors and affiliations

  • Joachim Cuntz
    • 1
  • Ralf Meyer
    • 2
  • Jonathan M. Rosenberg
    • 3
  1. 1.Mathematisches InstitutWestfälische Wilhelms-Universität MünsterMünsterGermany
  2. 2.Mathematisches InstitutGeorg-August-Universität GöttingenGöttingenGermany
  3. 3.Department of MathematicsUniversity of MarylandCollege ParkUSA

Bibliographic information