Taut foliations of 3-manifolds with Heegaard genus two

Abstract

Let $M$ be a closed, orientable, and irreducible 3-manifold with Heegaard genus two. We prove that if the fundamental group of $M$ is left-orderable then $M$ admits a co-orientable taut foliation.

arXiv comment44 pages, 23 figures. Duke Math Journal, to appear