420 research outputs found
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
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
The twisted Drinfeld double of a finite group via gerbes and finite groupoids
The twisted Drinfeld double (or quasi-quantum double) of a finite group with
a 3-cocycle is identified with a certain twisted groupoid algebra. The groupoid
is the loop (or inertia) groupoid of the original group and the twisting is
shown geometrically to be the loop transgression of the 3-cocycle. The twisted
representation theory of finite groupoids is developed and used to derive
properties of the Drinfeld double, such as representations being classified by
their characters.
This is all motivated by gerbes and 3-dimensional topological quantum field
theory. In particular the representation category of the twisted Drinfeld
double is viewed as the `space of sections' associated to a transgressed gerbe
over the loop groupoid.Comment: 25 pages, 10 picture
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
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