Forms and Foliations
In Section 4.4, 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) ⊆) 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.
KeywordsNormal Bundle Constant Rank Cochain Complex Grassmann Algebra Frobenius Theorem
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