Volume 19 (2015)

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Approximating $C^{1,0}$–foliations

William H Kazez and Rachel Roberts

Geometry & Topology Monographs 19 (2015) 21–72
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.

Keywords
contact structure, weakly symplectically fillable, tight, universally tight, dominating $2$–form, volume-preserving flow, taut foliation, confoliation, $L$–space
Primary: 57M50
Secondary: 53D10