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Topological and Bivariant K-Theory de Joachim Cuntz

Topological and Bivariant K-Theory: Oberwolfach Seminars, cartea 36

Autor Joachim Cuntz, Jonathan M. Rosenberg
en Limba Engleză Paperback – 19 iul 2007

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Specificații

ISBN-13: 9783764383985
ISBN-10: 3764383984
Pagini: 280
Ilustrații: XII, 262 p.
Dimensiuni: 170 x 242 x 15 mm
Greutate: 0.5 kg
Ediția:2007
Editura: Birkhäuser Basel
Colecția Birkhäuser
Seria Oberwolfach Seminars

Locul publicării:Basel, Switzerland

Public țintă

Research

Cuprins

The elementary algebra of K-theory.- Functional calculus and topological K-theory.- Homotopy invariance of stabilised algebraic K-theory.- Bott periodicity.- The K-theory of crossed products.- Towards bivariant K-theory: how to classify extensions.- Bivariant K-theory for bornological algebras.- A survey of bivariant K-theories.- Algebras of continuous trace, twisted K-theory.- Crossed products by ? and Connes’ Thom Isomorphism.- Applications to physics.- Some connections with index theory.- Localisation of triangulated categories.

Textul de pe ultima copertă

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.

Caracteristici

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 Includes supplementary material: sn.pub/extras