INTERSECTION PATTERNS OF ESSENTIAL SURFACES IN 3-MANIFOLDS

We study the intersection pattern of planes associated to an immersed incompressible surface in a 3-manifold. We establish the finite plane intersection property for immersed incompressible surfaces in certain 3-manifolds. For geometrically finite surfaces in closed, hyperbolic 3-manifolds, we show that there exists a finite cover of the surface cover in which all the sheets are embedded.