Topological and bivariant K-theory / Joachim Cuntz, Ralf Meyer, Jonathan M. Rosenberg
Tipo de material:
TextoSeries Oberwolfach seminars ; 36Detalles de publicación: Basel [etc.] : Birkhauser Verlag, 2007 Descripción: XI, 262 p. ; 24 cmISBN: 3-7643-8398-4Tema(s): Teoría k | Algebra | Topología algebraicaResumen: 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. 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. First available book on bivariant topological K-theory for algebras other than C*-algebras with complete proofs.Resumen: Índice: Preface.- The Elementary Algebra of K-theory.- Functional Calculusand Topological K-theory.- Homotopy Invariance of Stabilized Algebraic K-theory.- Bott periodicity.- K-theory of Crossed Products.- Bivariant K-theory.- Connections with Index Theory.- Localization of Triangulated Categories.- Algebras of Continuous Trace and Twisted K-theory.- Connes' Thom Isomorphism.- Applications to Physics.
| Tipo de ítem | Biblioteca de origen | Signatura | URL | Estado | Fecha de vencimiento | Código de barras | Reserva de ítems |
|---|---|---|---|---|---|---|---|
| Monografías | 02. BIBLIOTECA CAMPUS PUERTO REAL | 512.7/CUN/top (Navegar estantería(Abre debajo)) | Texto completo | Disponible Ubicación en estantería | Bibliomaps® | 3741963766 |
Índice
Bibliografía: p. [241]-247
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. 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. First available book on bivariant topological K-theory for algebras other than C*-algebras with complete proofs.
Índice: Preface.- The Elementary Algebra of K-theory.- Functional Calculusand Topological K-theory.- Homotopy Invariance of Stabilized Algebraic K-theory.- Bott periodicity.- K-theory of Crossed Products.- Bivariant K-theory.- Connections with Index Theory.- Localization of Triangulated Categories.- Algebras of Continuous Trace and Twisted K-theory.- Connes' Thom Isomorphism.- Applications to Physics.
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