Geometry & Topology

$C^0$ approximations of foliations

William Kazez and Rachel Roberts

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Abstract

Suppose that is a transversely oriented, codimension-one foliation of a connected, closed, oriented 3–manifold. Suppose also that has continuous tangent plane field and is taut; that is, closed smooth transversals to pass through every point of M. We show that if is not the product foliation S1 × S2, then can be C0 approximated by weakly symplectically fillable, universally tight contact structures. This extends work of Eliashberg and Thurston on approximations of taut, transversely oriented C2 foliations to the class of foliations that often arise in branched surface constructions of foliations. This allows applications of contact topology and Floer theory beyond the category of C2 foliated spaces.

Article information

Source
Geom. Topol., Volume 21, Number 6 (2017), 3601-3657.

Dates
Received: 3 January 2016
Accepted: 30 January 2017
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1510859327

Digital Object Identifier
doi:10.2140/gt.2017.21.3601

Mathematical Reviews number (MathSciNet)
MR3693573

Zentralblatt MATH identifier
1381.57014

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 53D10: Contact manifolds, general

Keywords
taut foliation holonomy contact topology weakly symplectically fillable universally tight

Citation

Kazez, William; Roberts, Rachel. $C^0$ approximations of foliations. Geom. Topol. 21 (2017), no. 6, 3601--3657. doi:10.2140/gt.2017.21.3601. https://projecteuclid.org/euclid.gt/1510859327


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