nonabelian bundle gerbe
Special and general types
A nonabelian bundle gerbe (as studied by Aschieri-Cantini-Jurco) is a model for the Lie groupoid which is the total space of a smooth -principal 2-bundle for the Lie 2-group that is the automorphism 2-group of a Lie group .
Specifically, a nonabelian bundle gerbe on a smooth manifold is given by a surjective submersion and an -bibundle together with a morphism of -bibundles
that is associative in the evident sense. This construction serves to model pullbacks of Lie 2-groupoids of the form
where on the rght we have the universal principal 2-bundle.
The resulting Lie groupoid is an extension of the Cech groupoid by . This generalizes the case of ordinary bundle gerbes, which are models for -principal 2-bundles, for the circle 2-group.
This can all be extended to topological groupoids, and to structure 2-groups given by more general crossed modules than .
Revised on September 9, 2010 07:43:30
by David Roberts