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arXiv · 1103.4815

Four Equivalent Versions of Non-Abelian Gerbes

Thomas Nikolaus·Konrad Waldorf
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Abstract

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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Thomas Nikolaus, Konrad Waldorf. 2013-07-17. Four Equivalent Versions of Non-Abelian Gerbes. https://arxiv.org/abs/1103.4815

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