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In mathematics, a taut foliation is a codimension 1 foliation of a 3-manifold with the property that there is a single transverse circle intersecting every leaf. By transverse circle, is meant a closed loop that is always transverse to the tangent field of the foliation. Equivalently, by a result of
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The last sentence is unclear because although it begins with "Equivalently," it uses the conjunction "if" rather than "if and only if". (There is a long tradition in mathematics of using "if" to mean "if and only if" in
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A Reebless foliation can fail to be taut but the only leaves of the foliation with no puncturing transverse circle must be compact, and in particular, homeomorphic to a torus.
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makes no sense to me. Even if it has some interpretation that I am missing, it should be reworded so that people don't have to struggle in order to understand it.
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Perhaps someone knowledgeable on a) this subject, b) English, and c) writing clearly will rephrase the problematic parts of this article.
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Dennis
Sullivan, a codimension 1 foliation is taut if there exists a Riemannian metric that makes each leaf a minimal surface.
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