Title: Finiteness of geodesic hypersurfaces in hyperbolic hybrids
Speaker: Nick Miller (Indiana University Bloomington)
Abstract: Both Reid and McMullen have independently asked whether a non-arithmetic hyperbolic 3-manifold necessarily contains only finitely many immersed geodesic surfaces. In this talk, I will discuss recent results where we show that a large class of non-arithmetic hyperbolic n-manifolds has only finitely many geodesic hypersurfaces, provided n is at least 3. Such manifolds are called hyperbolic hybrids and include the manifolds constructed by Gromov and Piatetski-Shapiro. These constitute the first examples of hyperbolic n-manifolds where the set of geodesic hypersurfaces is known to be finite and non-empty. I will also discuss the extension of these results to higher codimension. This is joint work with David Fisher, Jean-Francois Lafont, and Matthew Stover.
