Four Equivalent Versions of Non-Abelian Gerbes
Differential Geometry
2013-12-10 v3 Mathematical Physics
Category Theory
math.MP
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.
Keywords
Cite
@article{arxiv.1103.4815,
title = {Four Equivalent Versions of Non-Abelian Gerbes},
author = {Thomas Nikolaus and Konrad Waldorf},
journal= {arXiv preprint arXiv:1103.4815},
year = {2013}
}
Comments
65 pages, v2: minor corrections, new Corollary 7.2 about equivariant gerbes; v3: again minor corrections; v3 is the final and published version