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Sheaf theory for stacks in manifolds and twisted cohomology
for S¹–gerbes
Ulrich Bunke, Thomas Schick and Markus Spitzweck
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Algebraic & Geometric Topology 7
(2007) 1007–1062
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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 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.
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Keywords
sheaf theory, stacks, twisted
cohomology
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Mathematical Subject Classification
Primary: 46M20
Secondary: 14A20
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Publication
Received: 6 November 2006
Revised: 13 May 2007
Accepted: 15 May 2007
Published: 20 June 2007
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