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Dmitri Panov
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Francesco Lin
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Reebless and taut foliations

Suppose we are given a closed oriented 3-manifold. It is well known that taut foliations are Reebless, and if a Reebless foliation isn't taut then the leaves which don't admit a closed transversal are tori. Furthermore, it is straightforward that in a taut foliation all the closed leaves are homologically non trivial.

Conversely, is there any complete criterion to determine if a Reebless foliation is taut?