Geometry & Topology
- Geom. Topol.
- Volume 21, Number 6 (2017), 3601-3657.
$C^0$ approximations of foliations
Suppose that is a transversely oriented, codimension-one foliation of a connected, closed, oriented –manifold. Suppose also that has continuous tangent plane field and is taut; that is, closed smooth transversals to pass through every point of . We show that if is not the product foliation , then can be approximated by weakly symplectically fillable, universally tight contact structures. This extends work of Eliashberg and Thurston on approximations of taut, transversely oriented 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 foliated spaces.
Geom. Topol., Volume 21, Number 6 (2017), 3601-3657.
Received: 3 January 2016
Accepted: 30 January 2017
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 53D10: Contact manifolds, general
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