A global perspective to connections on principal 2-bundles
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.
Keywords
Cite
@article{arxiv.1608.00401,
title = {A global perspective to connections on principal 2-bundles},
author = {Konrad Waldorf},
journal= {arXiv preprint arXiv:1608.00401},
year = {2019}
}
Comments
42 pages. v2 comes with an additional lemma (2.2.5) about the pullback along a rank one map, and an additional section (5.4) providing a more thorough discussion of trivial bundles