Group negative curvature for 3–manifolds with genuine laminations

Abstract

We show that if a closed atoroidal 3–manifold $M$ contains a genuine lamination, then it is group negatively curved in the sense of Gromov. Specifically, we exploit the structure of the non-product complementary regions of the genuine lamination and then apply the first author’s Ubiquity Theorem to show that $M$ satisfies a linear isoperimetric inequality.