Twisted K-theory, old and new
arXiv:math/0701789
Abstract
Twisted K-theory has its origins in the author's PhD thesis [27] : http://www.numdam.org/item?id=ASENS_1968_4_1_2_161_0 and in the paper with P. Donovan http://www.numdam.org/item?id=PMIHES_1970__38__5_0 The objective of this paper is to revisit the subject in the light of generalizations and new developments inspired by Mathematical Physics. See for instance E. Witten (hep-th/9810188), J. Rosenberg http://anziamj.austms.org.au/JAMSA/V47/Part3/Rosenberg.html, C. Laurent-Gentoux, J.-L. Tu, P. Xu (math/0306138) and M.F. Atiyah, G. Segal (math/0407054), among many authors. The unifiyng theme in our presentation is the notion of K-theory of graded Banach algebras,implicit in [27], from which most of the classical theorems in twisted K-theory are derived. We also prove some new results in the subject : a Thom isomorphism in this setting, explicit computations in the equivariant case and new cohomology operations (in the graded and ungraded cases).
36 pages, see also http://www.math.jussieu.fr/~karoubi/. The revised version is better typed, contains minor revisions and more references. There is also a short historical survey of the subject at the end. To be published in the Proceedings of the conference in Valladolid on noncommutative geometry
References in corpus (5)
Cited by in corpus (11)
- A Stringy Product on Twisted Orbifold K-theory
- Twisted Morava K-theory and E-theory
- Twisted bundles and twisted K-theory
- The Real K-Theory of Compact Lie Groups
- Differential Twisted K-theory and Applications
- Twisted K-theory and obstructions against positive scalar curvature metrics
- Modular Invariants and Twisted Equivariant K-theory
- Topology of Fermi Surfaces and anomaly inflows
- A model of the twisted -theory related to bundles of finite order
- Dixmier-Douady for Dummies
- The index of families of projective operators