Algebraic & Geometric Topology

Sheaf theory for stacks in manifolds and twisted cohomology for $S^1$–gerbes

Ulrich Bunke, Thomas Schick, and Markus Spitzweck

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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 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.

Article information

Source
Algebr. Geom. Topol., Volume 7, Number 2 (2007), 1007-1062.

Dates
Received: 6 November 2006
Revised: 13 May 2007
Accepted: 15 May 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796712

Digital Object Identifier
doi:10.2140/agt.2007.7.1007

Mathematical Reviews number (MathSciNet)
MR2336247

Zentralblatt MATH identifier
1149.14002

Subjects
Primary: 46M20: Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) [See also 14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx]
Secondary: 14A20: Generalizations (algebraic spaces, stacks)

Keywords
sheaf theory stacks twisted cohomology

Citation

Bunke, Ulrich; Schick, Thomas; Spitzweck, Markus. Sheaf theory for stacks in manifolds and twisted cohomology for $S^1$–gerbes. Algebr. Geom. Topol. 7 (2007), no. 2, 1007--1062. doi:10.2140/agt.2007.7.1007. https://projecteuclid.org/euclid.agt/1513796712


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