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arXiv · 1608.00401

A global perspective to connections on principal 2-bundles

Konrad Waldorf
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Abstract

For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie groupoids, furnishing a differential graded-commutative Lie algebra equipped with an adjoint action of the Lie 2-group and a pullback operation along Morita equivalences between Lie groupoids. Using this notion, we define connections on principal 2-bundles as Lie 2-algebra-valued 1-forms on the total space Lie groupoid of the 2-bundle, satisfying a condition in complete analogy to connections on ordinary principal bundles. We carefully treat various notions of curvature, and prove a classification result by the non-abelian differential cohomology of Breen-Messing. This provides a consistent, global perspective to higher gauge theory.

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Konrad Waldorf. 2016-08-01. A global perspective to connections on principal 2-bundles. https://arxiv.org/abs/1608.00401

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