Title: Ubiquitous quasi-Fuchsian surfaces in cusped hyperbolic 3-manifolds,
Abstract: This paper proves that every finite volume hyperbolic 3-manifold M contains a
ubiquitous collection of closed, immersed, quasi-Fuchsian surfaces. These
surfaces are ubiquitous in the sense that their preimages in the universal
cover separate any pair of disjoint, non-asymptotic geodesic planes. The proof
relies in a crucial way on the corresponding theorem of Kahn and Markovic for
closed 3-manifolds. As a corollary of this result and a companion statement
about surfaces with cusps, we recover Wise's theorem that the fundamental group
of M acts freely and cocompactly on a CAT(0) cube complex.