Bundle gerbes

Details Bundle gerbes Bundle gerbes

1994-07-25

arxiv.org/abs/dg-ga/9407015v1

J.Lond.Math.Soc. 54 (1996) 403-416

Mathematics

Differential Geometry

19 pages

Scientific paper

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.

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