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

Research paper by Ulrich Bunke, Thomas Schick, Markus Spitzweck

Indexed on: 30 Aug '07Published on: 30 Aug '07Published in: Mathematics - K-Theory and Homology



Abstract

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.