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Sheaf theory for stacks in manifolds and twisted cohomology for S^1-gerbes

This is the first of a series of papers on sheaf theory on smooth and topological stacks and its applications. The main result of the present paper is the characterization of the twisted (by a closed integral three-form) de Rham complex on a manifold. As an object in the derived category it will be related with the push-forward of the constant sheaf from a S^1-gerbe with Dixmier-Douady class represented by the three-form. In order to formulate and prove this result we develop in detail the foundations of sheaf theory for smooth stacks.

preprint2007arXivOpen access
Ulrich BunkeThomas SchickMarkus Spitzweck
math.KT
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Ulrich BunkeThomas SchickMarkus Spitzweck

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