Four Equivalent Versions of Non-Abelian Gerbes

Details Four Equivalent Versions of Non-Abelian Gerbes Four Equivalent Versions of Non-Abelian Gerbes

2011-03-24

arxiv.org/abs/1103.4815v2

Mathematics

Differential Geometry

64 pages, v2: minor corrections, new Corollary 7.2 about equivariant gerbes

Scientific paper

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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