#### Volume 21, issue 6 (2017)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
$C^0$ approximations of foliations

### William H Kazez and Rachel Roberts

Geometry & Topology 21 (2017) 3601–3657
##### Abstract

Suppose that $\mathsc{ℱ}$ is a transversely oriented, codimension-one foliation of a connected, closed, oriented $3$–manifold. Suppose also that $\mathsc{ℱ}$ has continuous tangent plane field and is taut; that is, closed smooth transversals to $\mathsc{ℱ}$ pass through every point of $M$. We show that if $\mathsc{ℱ}$ is not the product foliation ${S}^{1}×{S}^{2}$, then $\mathsc{ℱ}$ can be ${C}^{0}$ approximated by weakly symplectically fillable, universally tight contact structures. This extends work of Eliashberg and Thurston on approximations of taut, transversely oriented ${C}^{2}$ 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 ${C}^{2}$ foliated spaces.

##### Keywords
taut foliation, holonomy, contact topology, weakly symplectically fillable, universally tight
Primary: 57M50
Secondary: 53D10