Seminars & Colloquia Calendar
Finiteness of maximal geodesic submanifolds of hyperbolic hybrids
Matthew Stover (Temple University)
Location: Hill 525
Date & time: Tuesday, 20 February 2018 at 3:30PM - 4:30PM
Abstract: Reid and McMullen have both asked whether or not the presence of infinitely many finite-volume totally geodesic surfaces in a hyperbolic 3-manifold implies arithmeticity of its fundamental group. I will explain why large classes of non-arithmetic hyperbolic n-manifolds, including the hybrids introduced by Gromov and Piatetski-Shapiro and many of their generalizations, have only finitely many finite-volume immersed totally geodesic hypersurfaces. These are the first examples of finite-volume n-hyperbolic manifolds, n>2, for which the collection of all finite-volume totally geodesic hypersurfaces is finite but nonempty. In this talk, I will focus mostly on dimension 3, where one can even construct link complements with this property.
This is joint work with David Fisher, Jean-François Lafont, and Nicholas Miller.