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ISSN (electronic): 1464-8997
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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 C2–foliations of 3–manifolds by both positive and negative contact structures to a large class of taut oriented C1,0–foliations, where by C1,0 foliation we mean a foliation with continuous tangent plane field. These C1,0–foliations can therefore be approximated by weakly symplectically fillable, universally tight, contact structures. This allows applications of C2–foliation theory to contact topology and Floer theory to be generalized and extended to constructions of C1,0–foliations.

Keywords
contact structure, weakly symplectically fillable, tight, universally tight, dominating $2$–form, volume-preserving flow, taut foliation, confoliation, $L$–space
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 53D10
References
Publication
Received: 13 November 2014
Accepted: 16 November 2014
Published: 29 December 2015
Authors
William H Kazez
Department of Mathematics
University of Georgia
Athens, GA 30602
USA
Rachel Roberts
Department of Mathematics
Washington University
1 Brookings Drive
St. Louis, MO 63130
USA