Thursday, July 18, 2013

1103.4815 (Thomas Nikolaus et al.)

Four Equivalent Versions of Non-Abelian Gerbes    [PDF]

Thomas Nikolaus, Konrad Waldorf
We recall and partially improve four versions of smooth, non-abelian gerbes: Cech cocycles, classifying maps, bundle gerbes, and principal 2-bundles. We prove that all these four versions are equivalent, and so establish new relations between interesting recent developments. Prominent partial results we prove are a bijection between continuous and smooth non-abelian cohomology, and an explicit equivalence between bundle gerbes and principal 2-bundles as 2-stacks.
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