Connections and curvings on lifting bundle gerbes
Abstract
Description
We construct a connection and a curving on a bundle gerbe associated with lifting a structure group of a principal bundle to a central extension. The construction is based on certain structures on the bundle, i.e. connections and splittings. The Deligne cohomology class of the lifting bundle gerbe with the connection and with the curving coincides with the obstruction class of the lifting problem with these structures.
18 pages, LaTeX; The definition of splitting is modified. Section 3 and 4 of the old version are united
18 pages, LaTeX; The definition of splitting is modified. Section 3 and 4 of the old version are united