Texas A&M University, Department of Mathematics, 216 Milner Hall, 1th of October 2003, 3:00-4:00

Groups and Dynamcs Seminar


On asymmetric hyperbolic manifolds

Alan Reid of University of Texas at Austin

Let M be a finite volume hyperbolic manifold. It is well-known that the full group of isometries of M is a finite group. In dimensions 2 and 3 it is known that every finite group arises as the full group of isometries of some closed hyperbolic 2 (resp 3) manifold. In particular, asymmetric manifolds exist in low-dimensions---a manifold is called asymmetric if the full isometry group is the trivial group. We will discuss existence of asymmetric closed hyperbolic n-manifolds in dimensions n > 3.