Topological and Bivariant K-Theory

• Κύριοι συγγραφείς: Cuntz, Joachim (Συγγραφέας), Meyer, Ralf (Συγγραφέας), Rosenberg, Jonathan M. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Basel : Birkhäuser Basel, 2007.
• Σειρά: Oberwolfach Seminars ; 36
• Θέματα: Mathematics.; K-theory.; Topology.; 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 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. 

 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.