Abstract

We extend the Eliashberg–Thurston theorem on approximations of taut oriented $C^2$–foliations of $3$–manifolds by both positive and negative contact structures to a large class of taut oriented $C^{1,0}$–foliations, where by $C^{1,0}$ foliation we mean a foliation with continuous tangent plane field. These $C^{1,0}$–foliations can therefore be approximated by weakly symplectically fillable, universally tight, contact structures. This allows applications of $C^2$–foliation theory to contact topology and Floer theory to be generalized and extended to constructions of $C^{1,0}$–foliations.

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Mathematical Subject Classification 2010

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