BUNDLE GERBES

Just as C-x principal bundles provide a geometric realisation of two-d imensional integral cohomology, gerbes or sheaves of groupoids, provid e a geometric realisation of three-dimensional integral cohomology thr ough their Dixmier-Douady class. I consider an alternative related geo metric realisation of three-dimensional cohomology called a bundle ger be. Every bundle gerbe gives rise to a gerbe and most of the well-know n examples of gerbes are bundle gerbes. I discuss the properties of bu ndle gerbes, in particular bundle gerbe connections and curvature and their associated Dixmier-Douady class.