Isometry group of Lorentz manifolds: A coarse perspective

We prove a structure theorem for the isometry group $${\text {Iso}}(M,g)$$ of compact Lorentz manifold, under assumption that closed subgroup has exponential growth. don’t assume anything about identity component , so our results apply discrete groups. infer full classification lattices can act isometrically on manifolds. Moreover, without any growth hypothesis, we Tits alternative subgroups .