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arXiv · 2102.09213

Isometry Group of Lorentz Manifolds: A Coarse Perspective

Charles Frances
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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).

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Charles Frances. 2021-02-18. Isometry Group of Lorentz Manifolds: A Coarse Perspective. https://arxiv.org/abs/2102.09213

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