Topological and Bivariant K-Theory

Joachim Cuntz‏ · Jonathan M. Rosenberg‏

אוק׳ 2007 · Oberwolfach Seminars ספר 36 · Springer Science & Business Media

מידע על הספר הדיגיטלי הזה

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.