1994/07/25 by Michael K. Murray · 1 voice · 1 citation
Mathematics · #dg-ga #math.DG
published as J.Lond.Math.Soc. 54 (1996) 403-416 · 19 pages
Just as \Cstar principal bundles provide a geometric realisation of two-dimensional integral cohomology; gerbes or sheaves of groupoids, provide a geometric realisation of three dimensional integral cohomology through their Dixmier-Douady class. I consider an alternative, related, geometric realisation of three dimensional cohomology called a bundle gerbe. Every bundle gerbe gives rise to a gerbe and most of the well-known examples examples of gerbes are bundle gerbes. I discuss the properties of bundle gerbes, in particular bundle gerbe connections and curvature and their associated Dixmier-Douady class.