Abstract
Suppose that is a transversely oriented, codimension-one foliation of a connected, closed, oriented –manifold. Suppose also that has continuous tangent plane field and is taut; that is, closed smooth transversals to pass through every point of . We show that if is not the product foliation , then can be approximated by weakly symplectically fillable, universally tight contact structures. This extends work of Eliashberg and Thurston on approximations of taut, transversely oriented foliations to the class of foliations that often arise in branched surface constructions of foliations. This allows applications of contact topology and Floer theory beyond the category of foliated spaces.
Citation
William Kazez. Rachel Roberts. "$C^0$ approximations of foliations." Geom. Topol. 21 (6) 3601 - 3657, 2017. https://doi.org/10.2140/gt.2017.21.3601
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