Topological and 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 a...
Auteurs principaux : | , , |
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Format : | Livre |
Langue : | anglais |
Titre complet : | Topological and Bivariant K-Theory / Joachim Cuntz, Ralf Meyer, Jonathan M. Rosenberg. |
Édition : | 1st ed. 2007. |
Publié : |
Basel :
Birkhäuser Basel
, [20..] Cham : Springer Nature |
Collection : | Oberwolfach Seminars (Online) ; 36 |
Accès en ligne : |
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Condition d'utilisation et de reproduction : | Conditions particulières de réutilisation pour les bénéficiaires des licences nationales : https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |
Contenu : | 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 |
Sujets : | |
Documents associés : | Autre format:
Topological and bivariant K-theory Autre format: Topological and Bivariant K-Theory Autre format: Topological and bivariant K-theory Autre format: Topological and Bivariant K-Theory Autre format: Topological and bivariant K-theory |
Résumé : | 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 |
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Notes : | L'impression du document génère 277 p. |
Bibliographie : | Bibliogr. Index |
ISBN : | 978-3-7643-8399-2 |
DOI : | 10.1007/978-3-7643-8399-2 |