Minimality of the action on the universal circle of uniform foliations

Sergio Fenley, Rafael Potrie

Given a uniform foliation by Gromov hyperbolic leaves on a 3-manifold, we show that the action of the fundamental group on the universal circle is minimal and transitive on pairs of different points. We also prove two other results: we prove that general uniform Reebless foliations are $\R$-covered and we give a new description of the universal circle of $\R$-covered foliations with Gromov hyperbolic leaves in terms of the JSJ decomposition of $M$.