Holonomy for Gerbes over Orbifolds

Abstract

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.

36 pages

References in corpus (4)

• Orbifolds as Groupoids: an Introduction
• Twisted Orbifold K-Theory
• Differential Characters on Orbifolds and String Connections I
• Deligne Cohomology for Orbifolds, discrete torsion and B-fields

Cited by in corpus (10)

• The twisted Drinfeld double of a finite group via gerbes and finite groupoids
• A Stringy Product on Twisted Orbifold K-theory
• A quantum Leray-Hirsch theorem for banded gerbes
• Differential Characters on Orbifolds and String Connections I
• Cyclification of Orbifolds
• Twisted loop transgression and higher Jandl gerbes over finite groupoids
• Supersymmetric field theories from twisted vector bundles
• An Introduction to Gerbes on Orbifolds
• Twisted Equivariant Tate K-Theory
• Orbifold String Topology