37 research outputs found
Deligne Cohomology for Orbifolds, discrete torsion and B-fields
In this paper we introduce the concept of Deligne cohomology of an orbifold.
We prove that the third Deligne cohomology group of a smooth \'{e}tale groupoid
classify gerbes with connection over the groupoid. We argue that the -field
and the discrete torsion in type II superstring theories are special kinds of
gerbes with connection, and finally, for each one of them, using Deligne
cohomology we construct a flat line bundle over the inertia groupoid, namely a
Ruan inner local in the case of an orbifold.Comment: To be published in the Proceedings of the Summer School "Geometric
and Topological methods for Quantum Field Theory", Villa de Leyva, Colombia
(2001
An Introduction to Gerbes on Orbifolds
This paper is a gentle introduction to some recent results involving the
theory of gerbes over orbifolds for topologists, geometers and physicists. We
introduce gerbes on manifolds, orbifolds, the Dixmier-Douady class,
Beilinson-Deligne orbifold cohomology, Cheeger-Simons orbifold cohomology and
string connections.Comment: To appear in the Annales Mathematiques Blaise Pasca
Holonomy for Gerbes over Orbifolds
In this paper we compute explicit formulas for the holonomy map for a gerbe
with connection over an orbifold. We show that the holonomy descends to a
transgression map in Deligne cohomology. We prove that this recovers both the
inner local systems in Ruan's theory of twisted orbifold cohomology and the
local system of Freed-Hopkins-Teleman in their work in twisted K-theory. In the
case in which the orbifold is simply a manifold we recover previous results of
Gawedzki and Brylinski.Comment: 36 page