Waldorf, Konrad (2012) Transgression to loop spaces and its inverse, III: Gerbes and thin fusion bundles. ADVANCES IN MATHEMATICS, 231 (6). pp. 3445-3472. ISSN 0001-8708,
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We show that the category of abelian gerbes over a smooth manifold is equivalent to a certain category of principal bundles over the free loop space. These principal bundles are equipped with fusion products and arc equivariant with respect to thin homotopies between loops. The equivalence is established by a functor called regression, and complements a similar equivalence for bundles and gerbes equipped with connections, derived previously in Part II of this series of papers. The two equivalences provide a complete loop space formulation of the geometry of gerbes; functorial, monoidal, natural in the base manifold, and consistent with passing from the setting "with connections" to the one "without connections". We discuss an application to lifting problems, which provides in particular loop space formulations of spin structures, complex spin structures, and spin connections. (C) 2012 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; Gerbes; Diffeological spaces; Holonomy; Loop space; Orientability of loop spaces; Complex spin structures; Transgression |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 30 Apr 2020 08:11 |
| Last Modified: | 30 Apr 2020 08:11 |
| URI: | https://pred.uni-regensburg.de/id/eprint/17587 |
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