Higher Poincare Lemma and Integrability

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.

1+21 pages, presentation streamlined, section on integrability for higher linear systems significantly improved, published version

References in corpus (1)

• Semistrict Higher Gauge Theory

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