Algebraic & Geometric Topology 7 (2007) 1007–1062

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 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

Primary: 46M20

Secondary: 14A20

References

Publication

Received: 6 November 2006
Revised: 13 May 2007
Accepted: 15 May 2007
Published: 20 June 2007

Authors