# Non-abelian differentiable gerbes

```@article{LaurentGengoux2009NonabelianDG,
title={Non-abelian differentiable gerbes},
author={Camille Laurent-Gengoux and Mathieu Sti{\'e}non and Ping Xu},
year={2009},
volume={220},
pages={1357-1427}
}```
• Published 29 November 2005
• Mathematics

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Journal of the Australian Mathematical Society
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## References

SHOWING 1-10 OF 53 REFERENCES

### Chern–Weil map for principal bundles over groupoids

• Mathematics
• 2004
The theory of principal G-bundles over a Lie groupoid is an important one unifying various types of principal G-bundles, including those over manifolds, those over orbifolds, as well as equivariant

### Bundle gerbes

. Just as C × principal bundles provide a geometric realisation of two-dimensional integral cohomology; gerbes or sheaves of groupoids, provide a geometric realisation of three dimensional integral

### The basic gerbe over a compact simple Lie group

Let \$G\$ be a compact, simply connected simple Lie group. We give a construction of an equivariant gerbe with connection on \$G\$, with equivariant 3-curvature representing a generator of \$H^3_G(G,\Z)\$.

### Sheaf theory for stacks in manifolds and twisted cohomology for S 1 -gerbes

• Mathematics
• 2007
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

### Nonabelian Bundle Gerbes, Their Differential Geometry and Gauge Theory

• Physics
• 2005
Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied

### Deformation quantization modules I:Finiteness and duality

• Mathematics
• 2008
We introduce the notion of being cohomologically complete for objects of the derived category of sheaves of \$Z[\hbar]\$-modules on a topological space. Then we consider a \$Z[\hbar]\$-algebra satisfying