1
$\begingroup$

In Eliashberg-Thurston's famous paper "Confoliations" Corollary 3.2.11, they proved that Irreducible three manifold with $b_{1}>0$ admits semi-fillable contact structure using Gabai's theorem in the paper ''Foliations and the topology of 3-manifolds'' about the existence of the taut foliation. But it seems that they require the foliation to be $C^{2}$ while I can't find this $C^{2}$ regularity in Gabai's paper. (Gabai showed that if $H_{2}$ is not generated by spheres and torus, then we can assume the foliation to be $C^{\infty}$.) So my question is why can they use Gabai's theorem in this case?

Improve this question
$\endgroup$
1
  • 2
    $\begingroup$ See "Approximating C^0-foliations" by Kazez and Roberts (arxiv.org/abs/1404.5919), which addresses exactly this issue. $\endgroup$
    – Steven Sivek
    Commented Feb 6, 2015 at 12:50

0

Reset to default

You must log in to answer this question.