Bunke, Ulrich and Nikolaus, Thomas and Voelkl, Michael (2016) Differential cohomology theories as sheaves of spectra. JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, 11 (1). pp. 1-66. ISSN 2193-8407, 1512-2891
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We show that every sheaf on the site of smooth manifolds with values in a stable (infinity, 1)-category (like spectra or chain complexes) gives rise to a "differential cohomology diagram" and a homotopy formula, which are common features of all classical examples of differential cohomology theories. These structures are naturally derived from a canonical decomposition of a sheaf into a homotopy invariant part and a piece which has a trivial evaluation on a point. In the classical examples the latter is the contribution of differential forms. This decomposition suggests a natural scheme to analyse new sheaves by determining these pieces and the gluing data. We perform this analysis for a variety of classical and not so classical examples.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; Differential cohomology; Sheaves on manifolds; Stable infinity categories |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Ulrich Bunke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 11 Mar 2019 14:30 |
| Last Modified: | 11 Mar 2019 14:30 |
| URI: | https://pred.uni-regensburg.de/id/eprint/2367 |
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