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Sheaf theory for stacks
in manifolds and twisted cohomology for $S^1$–gerbes
Ulrich Bunke, Thomas Schick and Markus Spitzweck |
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Algebraic & Geometric Topology 7 (2007) 1007–1062
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arXiv: math.KT/0603698 |
Abstract |
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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 gerbe over a smooth manifold is an object of the derived category of sheaves on . 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
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Mathematical Subject Classification 2000
Primary: 46M20
Secondary: 14A20
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References |
Publication
Received: 6 November 2006
Revised: 13 May 2007
Accepted: 15 May 2007
Published: 20 June 2007
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Authors |
| Ulrich Bunke | |
| NWF I - Mathematik Universität Regensburg 93040 Regensburg Germany |
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| Thomas Schick | |
| Mathematisches Institut Universität Göttingen Bunsenstr. 3-5 37073 Göttingen Germany |
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| Markus Spitzweck | |
| Mathematisches Institut Universität Göttingen Bunsenstr. 3-5 37073 Göttingen Germany |
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