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Differential cohomology theories as sheaves of spectra

Bunke, Ulrich ; Nikolaus, Thomas ; Völkl, Michael



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 ...

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