Twisted K-theory of differentiable stacks
| dc.creator | Tu, Jean-Louis | |
| dc.creator | Xu, Ping | |
| dc.creator | Laurent-Gengoux, Camille | |
| dc.date | 2003-06-08 | |
| dc.date | 2004-09-13 | |
| dc.date.accessioned | 2026-07-07T04:58:40Z | |
| dc.date.available | 2026-07-07T04:58:40Z | |
| dc.description | In this paper, we develop twisted $K$-theory for stacks, where the twisted class is given by an $S^1$-gerbe over the stack. General properties, including the Mayer-Vietoris property, Bott periodicity, and the product structure $K^i_α\otimes K^j_β\to K^{i+j}_{α+β}$ are derived. Our approach provides a uniform framework for studying various twisted $K$-theories including the usual twisted $K$-theory of topological spaces, twisted equivariant $K$-theory, and the twisted $K$-theory of orbifolds. We also present a Fredholm picture, and discuss the conditions under which twisted $K$-groups can be expressed by so-called "twisted vector bundles". Our approach is to work on presentations of stacks, namely \emph{groupoids}, and relies heavily on the machinery of $K$-theory ($KK$-theory) of $C^*$-algebras. | |
| dc.description | 74 pages | |
| dc.identifier | https://arxiv.org/abs/math/0306138 | |
| dc.identifier | http://arxiv.org/abs/math/0306138 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67734 | |
| dc.subject | K-Theory and Homology | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Differential Geometry | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L80 (Primary) 19K35,22A22,47L90,53-xx (Secondary) | |
| dc.title | Twisted K-theory of differentiable stacks | |
| dc.type | text |