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

Ulrich Bunke, Thomas Schick and Markus Spitzweck

Algebraic & Geometric Topology 7 (2007) 1007–1062

arXiv: math.KT/0603698

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.

Keywords
sheaf theory, stacks, twisted cohomology
Mathematical Subject Classification 2000
Primary: 46M20
Secondary: 14A20
References
Publication
Received: 6 November 2006
Revised: 13 May 2007
Accepted: 15 May 2007
Published: 20 June 2007
Authors
Ulrich Bunke
NWF I - Mathematik
Universität Regensburg
93040 Regensburg
Germany
Thomas Schick
Mathematisches Institut
Universität Göttingen
Bunsenstr. 3-5
37073 Göttingen
Germany
Markus Spitzweck
Mathematisches Institut
Universität Göttingen
Bunsenstr. 3-5
37073 Göttingen
Germany