Compact Lorentz manifolds with local symmetry

We prove a structure theorem for compact aspherical Lorentz manifolds with abundant local symmetry. If M is a compact, aspherical, real-analytic, complete Lorentz manifold such that the isometry group of the universal cover has semisimple identity component, then the local isometry orbits in M are roughly fibers of a fiber bundle. A corollary is that if M has an open, dense, locally homogeneous subset, then M is locally homogeneous. Acknowledgements: I thank my dissertation advisor, Benson Farb for his guidance and encouragement. I also thank Abdelghani Zeghib, with whom I had helpful conversations while working on this project. In loving memory of Laura Sue-Jung Kang