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2007 Sheaf theory for stacks in manifolds and twisted cohomology for $S^1$–gerbes
Ulrich Bunke, Thomas Schick, Markus Spitzweck
Algebr. Geom. Topol. 7(2): 1007-1062 (2007). DOI: 10.2140/agt.2007.7.1007

Abstract

In this paper we give a sheaf theory interpretation of the twisted cohomology of manifolds. To this end we develop a sheaf theory on smooth stacks. The derived push-forward of the constant sheaf with value along the structure map of a U(1) gerbe over a smooth manifold X is an object of the derived category of sheaves on X. Our main result shows that it is isomorphic in this derived category to a sheaf of twisted de Rham complexes.

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Ulrich Bunke. Thomas Schick. Markus Spitzweck. "Sheaf theory for stacks in manifolds and twisted cohomology for $S^1$–gerbes." Algebr. Geom. Topol. 7 (2) 1007 - 1062, 2007. https://doi.org/10.2140/agt.2007.7.1007

Information

Received: 6 November 2006; Revised: 13 May 2007; Accepted: 15 May 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1149.14002
MathSciNet: MR2336247
Digital Object Identifier: 10.2140/agt.2007.7.1007

Subjects:
Primary: 46M20
Secondary: 14A20

Rights: Copyright © 2007 Mathematical Sciences Publishers

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