Principal 2-bundles and their gauge 2-groups

Details Principal 2-bundles and their gauge 2-groups Principal 2-bundles and their gauge 2-groups

2008-03-26

arxiv.org/abs/0803.3692v4

Forum Math. 23 (3) 565-610, 2011

Mathematics

Differential Geometry

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

Scientific paper

10.1515/FORM.2011.020

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.

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