Holonomy for Gerbes over Orbifolds

Details Holonomy for Gerbes over Orbifolds Holonomy for Gerbes over Orbifolds

2003-07-09

arxiv.org/abs/math/0307114v1

J.Geom.Phys. 56 (2006) 1534-1560

Mathematics

Algebraic Topology

36 pages

Scientific paper

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.

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