G-gerbes, principal 2-group bundles and characteristic classes

Details G-gerbes, principal 2-group bundles and characteristic classes G-gerbes, principal 2-group bundles and characteristic classes

2008-01-08

arxiv.org/abs/0801.1238v2

Mathematics

Algebraic Topology

Presentation improved, references added and title changed; 27 pages

Scientific paper

We give an explicit description of a 1-1 correspondence between Morita equivalence classes of, on the one hand, principal 2-group $[G\to\Aut(G)]$-bundles over Lie groupoids (i.e. $[G\to\Aut(G)]$-bundles over differentiable stacks) and, on the other hand, central $G$-extensions of Lie groupoids (i.e. $G$-gerbes over differentiable stacks). We also introduce universal characteristic classes for 2-group bundles. For groupoid central $G$-extensions, we prove that the universal characteristic classes coincide with the Diximer Douady classes that can be computed from connection-type data.

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