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arXiv · 1406.5342

Higher Poincare Lemma and Integrability

Getachew Alemu Demessie·Christian Saemann
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Abstract

We prove the non-abelian Poincare lemma in higher gauge theory in two different ways. The first method uses a result by Jacobowitz which states solvability conditions for differential equations of a certain type. The second method extends a proof by Voronov and yields the explicit gauge parameters connecting a flat local connective structure to the trivial one. Finally, we show how higher flatness appears as a necessary integrability condition of a linear system which featured in recently developed twistor descriptions of higher gauge theories.

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Getachew Alemu Demessie, Christian Saemann. 2014-06-20. Higher Poincare Lemma and Integrability. https://doi.org/10.1063/1.4929537

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