Abundant Quasi-Fuchsian Surfaces in Cusped Hyperbolic 3-Manifolds

Daryl Cooper (UCSB)

Abstract

Suppose $M$ is a finite volume hyperbolic 3-manifold with al least one cusp. Given two disjoint hyperbolic planes $P$,$P^{\prime }$ in hyperbolic 3-space $H$ there is a closed quasi-Fuchsian surface in $M$ and a pre-image in $H$ that separates $P$ from $P^{\prime }$. This result is due to Kahn and Markovic when M is closed. Joint work with David Futer.