Nikolaus, Thomas and Schreiber, Urs and Stevenson, Danny (2015) Principal infinity-bundles: general theory. JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, 10 (4). pp. 749-801. ISSN 2193-8407, 1512-2891
Full text not available from this repository. (Request a copy)Abstract
The theory of principal bundles makes sense in any -topos, such as the -topos of topological, of smooth, or of otherwise geometric -groupoids/-stacks, and more generally in slices of these. It provides a natural geometric model for structured higher nonabelian cohomology and controls general fiber bundles in terms of associated bundles. For suitable choices of structure -group these -principal -bundles reproduce various higher structures that have been considered in the literature and further generalize these to a full geometric model for twisted higher nonabelian sheaf cohomology. We discuss here this general abstract theory of principal -bundles, observing that it is intimately related to the axioms that characterize -toposes. A central result is a natural equivalence between principal -bundles and intrinsic nonabelian cocycles, implying the classification of principal -bundles by nonabelian sheaf hyper-cohomology. We observe that the theory of geometric fiber -bundles associated to principal -bundles subsumes a theory of -gerbes and of twisted -bundles, with twists deriving from local coefficient -bundles, which we define, relate to extensions of principal -bundles and show to be classified by a corresponding notion of twisted cohomology, identified with the cohomology of a corresponding slice infinity-topos.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | LIFTING PROBLEMS; K-THEORY; GERBES; 2-GERBES; Nonabelian cohomology; Higher topos theory; Principal bundles |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 06 May 2019 07:25 |
| Last Modified: | 06 May 2019 07:25 |
| URI: | https://pred.uni-regensburg.de/id/eprint/4417 |
Actions (login required)
 |
View Item |
