## 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 $$P$$,$$P'$$ in hyperbolic 3-space $$H$$ there is a closed quasi-Fuchsian surface in $$M$$ and a pre-image in $$H$$ that separates $$P$$ from $$P'$$. This result is due to Kahn and Markovic when M is closed. Joint work with David Futer.