Compact Lorentz manifolds with local symmetry

Many important classes of compact manifolds, such as hyperbolic
manifolds, have paltry isometry group but abundant local symmetry. I will
present a structure theorem for compact aspherical Lorentz manifolds with
abundant local symmetry. This result is analogous to a theorem of Farb
and Weinberger on compact aspherical Riemannian manifolds. Some tools
that will be discussed are Gromov’s stratification for rigid geometric
structures and rational cohomological dimension.