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

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

2006-03-30

arxiv.org/abs/math/0603698v3

Algebraic & Geometric Topology 7 (2007) 1007-1062

Mathematics

K-Theory and Homology

39 pages, v2 typos corrected and references added. v3 confusion in 2.2.5 cleaned up

Scientific paper

10.2140/agt.2007.7.1007

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.

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