Uniform 1-Cochains and Genuine Laminations

Abstract

We construct a pair of transverse genuine laminations on an atoroidal 3-manifold admitting transversely orientable uniform 1-cochain. The laminations are induced by the uniform 1-cochain and they are indeed the "straightening" of the coarse laminations defined in [Ca], by using minimal surface techniques. Moreover, when you collapse these laminations, you can get a topological pseudo-Anosov flow, as defined by Mosher, [Mo].