English

Isometry Group of Lorentz Manifolds: A Coarse Perspective

Differential Geometry 2021-02-19 v1 Group Theory

Abstract

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

Keywords

Cite

@article{arxiv.2102.09213,
  title  = {Isometry Group of Lorentz Manifolds: A Coarse Perspective},
  author = {Charles Frances},
  journal= {arXiv preprint arXiv:2102.09213},
  year   = {2021}
}