Topological and Bivariant K-Theory
Springer Basel (Verlag)
978-3-7643-8398-5 (ISBN)
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.
| Erscheint lt. Verlag | 19.7.2007 |
|---|---|
| Reihe/Serie | Oberwolfach Seminars |
| Zusatzinfo | XII, 262 p. |
| Verlagsort | Basel |
| Sprache | englisch |
| Maße | 170 x 242 mm |
| Gewicht | 530 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Schlagworte | functional calculus • Hardcover, Softcover / Mathematik/Arithmetik, Algebra • HC/Mathematik/Arithmetik, Algebra • Homotopy • K-Theorie • K-theory • Thom isomorphism • topological invariants |
| ISBN-10 | 3-7643-8398-4 / 3764383984 |
| ISBN-13 | 978-3-7643-8398-5 / 9783764383985 |
| Zustand | Neuware |
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