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arXiv · 1311.3188

Differential cohomology theories as sheaves of spectra

Ulrich Bunke·Thomas Nikolaus·Michael Völkl
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Abstract

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 suggest 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.

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Ulrich Bunke, Thomas Nikolaus, Michael Völkl. 2013-11-13. Differential cohomology theories as sheaves of spectra. https://arxiv.org/abs/1311.3188

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