Department of Mathematics - Master Calendar

Embedded essential surfaces in a 3-manifold correspond to non-trivial splittings of its fundamental group. We give some conditions on the fundamental group of a Haken hyperbolic 3-manifold which guarantee that any other 3-manifold group with the same finite quotients must have a non-trivial splitting. Using one of these conditions, we obtain restrictions on the possible first Betti numbers of regular covers of aspherical integer homology spheres. This is joint work with Khánh Lê.