Forms and Foliations

Part of the Birkhäuser Advanced Texts / Basler Lehrbücher book series


In Section 4.5, we proved the vector field version of the Frobenius integrability theorem: a k-plane field E on a manifold M is integrable if and only if Γ(E) \( \subseteq \mathfrak{X} \)(M) is a Lie subalgebra. In this chapter, we develop an equivalent version of this theorem, stated in terms of the Grassmann algebra A*(M) of differential forms. Useful consequences of this point of view will be treated.


Normal Bundle Constant Rank Cochain Complex Frobenius Theorem Vector Field Version 
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© Birkhäuser Boston 2008

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