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.