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Holonomy for gerbes over orbifolds

Institution:	1. Departamento de Matemáticas, CINVESTAV, Apartado Postal 14-740, México D.F. 07000, México;2. Departamento de Matemáticas, Universidad de los Andes, Carrera 1 N. 18A-10 Bogotá, Colombia;1. Universidade Federal do Paraná, Departamento de Matemática, C.P. 019081, 81531-990 Curitiba, PR, Brazil;2. Université Paris Diderot, Sorbonne Paris Cité, IMJ-PRG, CNRS, UMR 7586, 75013 Paris, France;3. Department of Mathematics, University of North Carolina at Chapel Hill – UNC-CH, Chapel Hill, NC 27599-3250, United States;1. Departamento de Álgebra, Geomtría y Topología, Universidad de Málaga, 29071-Málaga, Spain;2. Fakultät für Mathematik, Universität Regensburg, D-93040 Regensburg, Germany;1. School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa;2. Dipartimento di Scienze Matematiche “G.L. Lagrange”, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy;3. School of Mathematical Sciences, University of Adelaide, SA 5005, Australia

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 1] and the local system of Freed–Hopkins–Teleman in their work in twisted K-theory 2]. In the case in which the orbifold is simply a manifold we recover previous results of Gaw?dzki 3] and Brylinski4].

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