Non Abelian Differentiable Gerbes
Differential Geometry
2009-03-20 v5 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
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 -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 -gerbes over stacks. We also introduce -central extensions of groupoids, generalizing the standard groupoid -central extensions. As an example, we apply our theory to study the differential geometry of -gerbes over a manifold.
Cite
@article{arxiv.math/0511696,
title = {Non Abelian Differentiable Gerbes},
author = {Camille Laurent-Gengoux and Mathieu Stienon and Ping Xu},
journal= {arXiv preprint arXiv:math/0511696},
year = {2009}
}
Comments
67 pages, references added and updated, final version to appear in Adv. Math