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.