Non Abelian Differentiable Gerbes

Details Non Abelian Differentiable Gerbes Non Abelian Differentiable Gerbes

2005-11-29

arxiv.org/abs/math/0511696v5

Advances in Mathematics 220 (2009) 1357-1427

Mathematics

Differential Geometry

67 pages, references added and updated, final version to appear in Adv. Math

Scientific paper

10.1016/j.aim.2008.10.018

We study non-abelian differentiable gerbes over stacks using the theory of Lie groupoids. More precisely, we develop the theory of connections on Lie groupoid $G$-extensions, which we call "connections on gerbes", and study the induced connections on various associated bundles. We also prove analogues of the Bianchi identities. In particular, we develop a cohomology theory which measures the existence of connections and curvings for $G$-gerbes over stacks. We also introduce $G$-central extensions of groupoids, generalizing the standard groupoid $S^1$-central extensions. As an example, we apply our theory to study the differential geometry of $G$-gerbes over a manifold.

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