Schreiber, Urs and Waldorf, Konrad (2011) SMOOTH FUNCTORS VS. DIFFERENTIAL FORMS. HOMOLOGY HOMOTOPY AND APPLICATIONS, 13 (1). pp. 143-203. ISSN 1532-0073,
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We establish a relation between smooth 2-functors defined on the path 2-groupoid of a smooth manifold and differential forms on this manifold. This relation can be understood as a part of a dictionary between fundamental notions from category theory and differential geometry. We show that smooth 2-functors appear in several fields, namely as connections on (non-abelian) gerbes, as derivatives of smooth functors and as critical points in BF theory. We demonstrate further that our dictionary provides a powerful tool to discuss the transgression of geometric objects to loop spaces.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PARALLEL TRANSPORT; GERBES; HOLONOMY; connection; gerbe; 2-group; path 2-groupoid; parallel transport |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 30 Jun 2020 10:18 |
| Last Modified: | 30 Jun 2020 10:18 |
| URI: | https://pred.uni-regensburg.de/id/eprint/21591 |
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