Taut foliations
Abstract
We describe notions of tautness that arise in the study of C0 foliations, C1,0 or smoother foliations, and in geometry. We give examples to show that these notions are different, and discuss how these differences impact some classical foliation results. We construct examples of smoothly taut C∞,0 foliations that can be C0 approximated by both weakly symplectically fillable, universally tight contact structures and by overtwisted contact structures.
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