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Bundle Gerbes
Author(s) -
Murray M. K.
Publication year - 1996
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/54.2.403
Subject(s) - bundle , realisation , mathematics , pure mathematics , principal bundle , class (philosophy) , cohomology , connection (principal bundle) , frame bundle , curvature , normal bundle , vector bundle , computer science , geometry , physics , materials science , quantum mechanics , artificial intelligence , composite material
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.