We prove a structure theorem for the isometry group \({\text {Iso}}(M,g)\) 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 \({\text {Iso}}(M,g)\), 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 \({\text {Iso}}(M,g)\).

中文翻译：

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洛伦兹流形的等距群：粗略透视

我们证明了紧致洛伦兹流形的等距群\({\text {Iso}}(M,g)\)的结构定理，假设封闭子群具有指数增长。我们不对\({\text {Iso}}(M,g)\)的恒等分量做任何假设，因此我们的结果适用于离散等距组。我们推断出可以在紧凑洛伦兹流形上等距作用的格子的完整分类。此外，在没有任何增长假设的情况下，我们证明了\({\text {Iso}}(M,g)\) 的离散子群的 Tits 替代方案。