Principal 2-bundles and their gauge 2-groups

Abstract

In this paper we introduce principal 2-bundles and show how they are classified by non-abelian Cech cohomology. Moreover, we show that their gauge 2-groups can be described by 2-group-valued functors, much like in classical bundle theory. Using this, we show that, under some mild requirements, these gauge 2-groups possess a natural smooth structure. In the last section we provide some explicit examples.

40 pages; v3: completely revised and extended, classification corrected, name changed, to appear in Forum Math

References in corpus (5)

• Integrating L-infinity algebras
• Lie Group Structures on Symmetry Groups of Principal Bundles
• Equivalences of Smooth and Continuous Principal Bundles with Infinite-Dimensional Structure Group
• Obstruction classes of crossed modules of Lie algebroids and Lie groupoids linked to existence of principal bundles
• Central extensions of groups of sections

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