Leaf topology of minimal hyperbolic foliations with non simply-connected generic leaf

Abstract

A noncompact (oriented) surface satisfies the condition ( ⋆ ) (\star ) if their isolated ends are accumulated by genus. We show that every surface satisfying this condition is homeomorphic to the leaf of a minimal codimension one foliation on a closed 3 3 -manifold whose generic leaf is not simply connected. Moreover, the above result is also true for any prescription of a countable family of noncompact surfaces (satisfying ( ⋆ ) (\star ) ): they can coexist in the same minimal codimension one foliation as above. All the given examples are hyperbolic foliations, meaning that they admit a leafwise Riemannian metric of constant negative curvature.