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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 : | , , |
|---|---|
| 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 |
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| 200 | 1 | |a Topological and Bivariant K-Theory |f Joachim Cuntz, Ralf Meyer, Jonathan M. Rosenberg. | |
| 205 | |a 1st ed. 2007. | ||
| 214 | 0 | |a Basel |c Birkhäuser Basel | |
| 214 | 2 | |a Cham |c Springer Nature |d [20..] | |
| 225 | 0 | |a Oberwolfach Seminars |x 2296-5041 |v 36 | |
| 303 | |a L'impression du document génère 277 p. | ||
| 320 | |a Bibliogr. Index | ||
| 327 | 1 | |a The elementary algebra of K-theory |a Functional calculus and topological K-theory |a Homotopy invariance of stabilised algebraic K-theory |a Bott periodicity |a The K-theory of crossed products |a Towards bivariant K-theory: how to classify extensions |a Bivariant K-theory for bornological algebras |a A survey of bivariant K-theories |a Algebras of continuous trace, twisted K-theory |a Crossed products by ? and Connes Thom Isomorphism |a Applications to physics |a Some connections with index theory |a Localisation of triangulated categories | |
| 330 | |a 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 | ||
| 371 | 0 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | |
| 371 | 0 | |a Accès soumis à abonnement pour tout autre établissement | |
| 371 | 1 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales |c https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | |
| 410 | | | |0 158175158 |t Oberwolfach Seminars (Online) |x 2296-5041 |v 36 | |
| 452 | | | |0 118145967 |t Topological and bivariant K-theory |f Joachim Cuntz, Ralf Meyer, Jonathan M. Rosenberg |c Basel |n Birkhauser |d 2007 |p 1 vol. (XI-262 p.) |s Oberwolfach seminars |y 3-7643-8398-4 | |
| 452 | | | |t Topological and Bivariant K-Theory |b Texte imprimé |y 9783764392024 | |
| 452 | | | |0 118145967 |t Topological and bivariant K-theory |f Joachim Cuntz, Ralf Meyer, Jonathan M. Rosenberg |c Basel |n Birkhauser |d 2007 |p 1 vol. (XI-262 p.) |s Oberwolfach seminars |y 3-7643-8398-4 | |
| 452 | | | |t Topological and Bivariant K-Theory |b Texte imprimé |y 9783764392024 | |
| 452 | | | |0 118145967 |t Topological and bivariant K-theory |f Joachim Cuntz, Ralf Meyer, Jonathan M. Rosenberg |c Basel |n Birkhauser |d 2007 |p 1 vol. (XI-262 p.) |s Oberwolfach seminars |y 3-7643-8398-4 | |
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| 606 | |3 PPN027720012 |a Topologie algébrique |2 rameau | ||
| 606 | |3 PPN032351151 |a Index, Théorie de l' (mathématiques) |2 rameau | ||
| 606 | |3 PPN031439322 |a Théorèmes d'indices |2 rameau | ||
| 606 | |3 PPN032721293 |a Atiyah-Singer, Théorème d' |2 rameau | ||
| 606 | |3 PPN027506967 |a K-théorie |2 rameau | ||
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