We investigate conformal actions of cocompact lattices in higher-rank simple Lie groups on compact pseudo-Riemannian manifolds. Our main result gives a general bound on the real-rank of the lattice, which was already known for the action of the full Lie group by a result of Zimmer. When the real-rank is maximal, we prove that the manifold is conformally flat. This indicates that a global conclusion similar to that of Bader, Nevo and Frances, Zeghib in the case of a Lie group action might be obtained. We also give better estimates for actions of cocompact lattices in exceptional groups. Our work is strongly inspired by the recent breakthrough of Brown, Fisher and Hurtado on Zimmer’s conjecture.

中文翻译：

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紧拟黎曼流形上高阶格的保形作用

我们研究紧伪伪黎曼流形上高阶简单Lie群中共紧格的共形作用。我们的主要结果给出了格的实秩的一个一般界限，齐默的结果已经为整个李氏群的作用所知。当实数为最大时，我们证明流形是共形的。这表明，对于李群诉讼，可能获得类似于Bader，Nevo和Frances，Zeghib的全局结论。我们还为例外群体中的共紧晶格的作用提供了更好的估计。布朗，费舍尔和赫塔多在齐默的猜想上的最新突破，极大地激发了我们的工作。