Vol. 264, No. 2, 2013

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Four equivalent versions of nonabelian gerbes

Thomas Nikolaus and Konrad Waldorf

Vol. 264 (2013), No. 2, 355–420
Abstract

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

Keywords
nonabelian gerbe, principal 2-bundle, 2-group, nonabelian cohomology, 2-stack
Mathematical Subject Classification 2010
Primary: 55R65
Secondary: 53C08, 55N05, 22A22
Milestones
Received: 23 April 2012
Accepted: 19 November 2012
Published: 28 July 2013
Authors
Thomas Nikolaus
Fachbereich Mathematik
Bereich Algebra und Zahlentheorie
Universität Hamburg
Bundesstraße 55
D-20146 Hamburg
Germany
Konrad Waldorf
Fakultät für Mathematik
Universität Regensburg
Universitätsstraße 31
D-93053 Regensburg
Germany