Topological and Bivariant K-Theory (Oberwolfach Seminars)
Edition: 1 edition
Publisher: Birkhäuser Basel; Birkhauser
Published: September 14, 2007
Language: eng
Format: Paperback
Number of pages: 262
ISBN-13: 9783764383985
Subjects: Algebraic topology; Mathematics; Science/Mathematics; Algebra - General; K-Theory; Mathematics / Algebra / General; Thom isomorphism; functional calculus; topological invariants; Topology - General
Description: 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.