Seminar

Arithmetic lattices of simplest type in Isom(H^n) are a special class of arithmetic lattices, and are the only arithmetic lattices in even dimensions. The quotient spaces are arithmetic hyperbolic n-manifolds with infinitely many properly immersed totally geodesic co-dimension one submanifolds, and have many other nice properties. Such lattices have many applications in building examples of special negatively curved manifolds and discrete subgroups of Isom(H^n), for instance in works of Gromov-Piatetski-Shapiro, Gromov-Thurston, Agol, etc. I will start by introducing the construction of these lattices, and discuss some properties and applications.