Maximal Symmetry Groups of Hyperbolic three-manifolds

Abstract

Every nite group acts as the full isometry group of some compact hyperbolic 3-manifold. In this paper we study those nite groups which act maximally, that is when the ratio jIsom+(M)j=vol(M)is maximal among all such manifolds. In two dimensions maximal symmetry groups are called Hurwitz groups, and arise as quotients of the (2,3,7){triangle group. Here we study quotients of the minimal co-volume lattice.