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

Bunke, Ulrich¹ ; Schick, Thomas² ; Spitzweck, Markus²

¹NWF I - Mathematik, Universität Regensburg, 93040 Regensburg, Germany
²Mathematisches Institut, Universität Göttingen, Bunsenstr. 3-5, 37073 Göttingen, Germany

Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 1007-1062

Résumé

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.

Détail

DOI : 10.2140/agt.2007.7.1007

Keywords: sheaf theory, stacks, twisted cohomology

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