Approximating $C^{1,0}$-foliations

William H. Kazez; Rachel Roberts

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arXiv · 1404.5919

Approximating $C^{1,0}$-foliations

William H. Kazez·Rachel Roberts

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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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BibTeX RIS

William H. Kazez, Rachel Roberts. 2014-04-20. Approximating $C^{1,0}$-foliations. https://arxiv.org/abs/1404.5919

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