Sheaf theory for stacks in manifolds and twisted cohomology for S1–gerbes

Bunke, Ulrich; Schick, Thomas; Spitzweck, Markus

doi:10.2140/agt.2007.7.1007

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ISSN (electronic): 1472-2739

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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

DOI: 10.2140/agt.2007.7.1007

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 $ℝ$ 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

Volume 7, issue 2 (2007)