Nikolaus, Thomas and Waldorf, Konrad (2013) Lifting problems and transgression for non-abelian gerbes. ADVANCES IN MATHEMATICS, 242. pp. 50-79. ISSN 0001-8708,
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We discuss lifting and reduction problems for bundles and gerbes in the context of a Lie 2-group. We obtain a geometrical formulation (and a new proof) for the exactness of Breen's long exact sequence in non-abelian cohomology. We use our geometrical formulation in order to define a transgression map in non-abelian cohomology. This transgression map relates the degree one non-abelian cohomology of a smooth manifold (represented by non-abelian gerbes) with the degree zero non-abelian cohomology of the free loop space (represented by principal bundles). We prove several properties for this transgression map. For instance, it reduces - in case of a Lie 2-group with a single object to the ordinary transgression in ordinary cohomology. We describe applications of our results to string manifolds: first, we obtain a new comparison theorem for different notions of string structures. Second, our transgression map establishes a direct relation between string structures and spin structures on the loop space. (C) 2013 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | BUNDLE GERBES; DIFFERENTIAL GEOMETRY; STRING 2-GROUP; LOOP SPACE; MODELS; Non-abelian gerbe; Non-abelian cohomology; Lie 2-group; Transgression; Loop space; String structure |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 06 Apr 2020 11:44 |
| Last Modified: | 06 Apr 2020 11:44 |
| URI: | https://pred.uni-regensburg.de/id/eprint/16345 |
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