Contact perturbations of Reebless foliations are universally tight (Q342692)

This paper presents a complete proof of the following result:NEWLINENEWLINETheorem. Let \(\mathcal F\) be a Reebless foliation on a closed 3-manifold \(M\). Then there is a \(C^0\)-neighborhood \({\mathcal U}_0\) of \(T{\mathcal F}\) in the space of smooth plane fields such that any contact structure \(\xi\) in \({\mathcal U}_0\) is universally tight.NEWLINENEWLINEThis result was stated in the book [\textit{Ya. M. Eliashberg} and \textit{W. P. Thurston}, Confoliations. Providence, RI: American Mathematical Society (1998; Zbl 0893.53001)], but the proof there was not complete.NEWLINENEWLINEThe concluding section of this paper compares some differing notions of tightness for confoliations.