Twisted $K$-theory
| dc.creator | Atiyah, Michael | |
| dc.creator | Segal, Graeme | |
| dc.date | 2004-07-05 | |
| dc.date | 2005-10-31 | |
| dc.date.accessioned | 2026-07-07T06:38:38Z | |
| dc.date.available | 2026-07-07T06:38:38Z | |
| dc.description | Twisted complex $K$-theory can be defined for a space $X$ equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C$^*$-algebras. Up to equivalence, the twisting corresponds to an element of $H^3(X;\Z)$. We give a systematic account of the definition and basic properties of the twisted theory, emphasizing some points where it behaves differently from ordinary $K$-theory. (We omit, however, its relations to classical cohomology, which we shall treat in a sequel.) We develop an equivariant version of the theory for the action of a compact Lie group, proving that then the twistings are classified by the equivariant cohomology group $H^3_G(X;\Z)$. We also consider some basic examples of twisted $K$-theory classes, related to those appearing in the recent work of Freed-Hopkins-Teleman. | |
| dc.description | 49 pages;some minor corrections have been made to the earlier version | |
| dc.identifier | https://arxiv.org/abs/math/0407054 | |
| dc.identifier | http://arxiv.org/abs/math/0407054 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100804 | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 55N15 | |
| dc.title | Twisted $K$-theory | |
| dc.type | text |