Bundle Gerbes

1996/10/01 by M. K. Murray, Michael K. Murray · 8 citations
Mathematics · Medicine · #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra #Cancer Treatment and Pharmacology

paper · doi:10.1112/jlms/54.2.403

Abstract

Just as C× 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 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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