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Foliation


Let M^n be an n-manifold and let F={F_alpha} denote a partition of M^n into disjoint pathwise-connected subsets. Then F is called a foliation of M^n of codimension c (with 0<c<n) if there exists a cover of M^n by open sets U, each equipped with a homeomorphism h:U->R^n or h:U->R_+^n which throws each nonempty component of F_alpha intersection U onto a parallel translation of the standard hyperplane R^(n-c) in R^n. Each F_alpha is then called a foliation leaf and is not necessarily closed or compact (Rolfsen 1976, p. 284).


See also

Confoliation, Cover, Foliation Leaf, Homeomorphism, Manifold, Reeb Foliation

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References

Candel, A. and Conlon, L. Foliations I. Providence, RI: Amer. Math. Soc., 1999.Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, 1976.

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Foliation

Cite this as:

Weisstein, Eric W. "Foliation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Foliation.html

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