Approximating $C^0$-foliations by contact structures

Abstract

We show that any co-orientable foliation of dimension two on a closed orientable $3$-manifold with continuous tangent plane field can be $C^0$-approximated by both positive and negative contact structures unless all the leaves are simply connected. As applications we deduce that the existence of a taut $C^0$-foliation implies the existence of universally tight contact structures in the same homotopy class of plane fields and that a closed $3$-manifold that admits a taut $C^0$-foliation of codimension-1 is not an $L$-space in the sense of Heegaard-Floer homology.

35 pages; 8 figures; Improved exposition following Referee's suggestions (To appear in Geom. Funct. Anal.)

References in corpus (2)

• A Hölder continuous vector field tangent to many foliations
• Taut foliations

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