, Volume 245, Issue 3, pp 449-489
Date: 06 Feb 2004

Gerbes over Orbifolds and Twisted K-Theory

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Abstract

In this paper we construct an explicit geometric model for the group of gerbes over an orbifold X. We show how from its curvature we can obtain its characteristic class in H 3(X) via Chern-Weil theory. For an arbitrary gerbe , a twisting K orb(X) of the orbifold K-theory of X is constructed, and shown to generalize previous twisting by Rosenberg [28], Witten [35], Atiyah-Segal [2] and Bowknegt et. al. [4] in the smooth case and by Adem-Ruan [1] for discrete torsion on an orbifold.

Communicated by A. Connes
The first author was partially supported by the National Science Foundation and Conacyt-México