当前位置: X-MOL 学术Geom. Funct. Anal. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Isometry group of Lorentz manifolds: A coarse perspective
Geometric and Functional Analysis ( IF 2.4 ) Pub Date : 2021-11-30 , DOI: 10.1007/s00039-021-00585-1
Charles Frances 1
Affiliation  

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:

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。

更新日期:2021-12-01
down
wechat
bug