Forms and Foliations

  • Lawrence Conlon
Part of the Birkhäuser Advanced Texts book series (BAT)


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.


Normal Bundle Constant Rank Cochain Complex Grassmann Algebra Frobenius Theorem 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Lawrence Conlon
    • 1
  1. 1.Department of MathematicsWashington UniversitySt. LouisUSA

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