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Foliation

المؤلف:  Candel, A. and Conlon, L

المصدر:  Foliations I. Providence, RI: Amer. Math. Soc., 1999.

الجزء والصفحة:  ...

20-7-2021

2349

Foliation

Let  be an -manifold and let {F_alpha}" src="https://mathworld.wolfram.com/images/equations/Foliation/Inline3.gif" style="height:15px; width:52px" /> denote a partition of  into disjoint pathwise-connected subsets. Then  is called a foliation of  of codimension  (with ) if there exists a cover of  by open sets , each equipped with a homeomorphism  or  which throws each nonempty component of  onto a parallel translation of the standard hyperplane  in . Each  is then called a foliation leaf and is not necessarily closed or compact (Rolfsen 1976, p. 284).

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.