group cohomology, nonabelian group cohomology, Lie group cohomology
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A bundle 2-gerbe is a special presentation of the total space of a -principal 3-bundle, where is the circle Lie 3-group.
A connection on a bundle 2-gerbe is a special cocycle representative for circle n-bundles with connection, hence for degree 4 Deligne cohomology, hence for degree 4 Cheeger-Simons differential characters.
The definition is built by iteration on the definition of bundle gerbe:
a bundle 2-gerbe over a manifold is
a surjective submersion ;
on the fiber product a bundle gerbe ;
a morphims of bundle gerbes ;
which is associative up to a choice of coherent 2-morphisms.
principal 3-bundle / 2-gerbe / bundle 2-gerbe
Bundle 2-gerbes were briefly introduced in
Volume 21, Issue 2, January 1997, Pages 183-197 (arXiv:hep-th/9511169, doi:10.1016/S0393-0440(96)00014-9)
and further developed in
drawing on ideas from Stevenson’s PhD thesis (arXiv:math/0004117).
A general picture of bundle -gerbes (with connection) as circle (n+1)-bundles with connection classified by Deligne cohomology is in
A model for the supergravity C-field in terms of nonabelian bundle 2-gerbes:
Last revised on February 8, 2024 at 13:45:07. See the history of this page for a list of all contributions to it.