Invariant measures and measurable projective factors for actions of higher-rank lattices on manifolds

• 成果类型: Article
• 署名作者: Brown, Aaron; Hertz, Federico; Wang, Zhiren
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2022.196.3.2
• 发表日期: 2022
• 页码: 941-981
• 关键词: metric entropy; RIGIDITY; diffeomorphisms; distortion

摘要

We consider smooth actions of lattices in higher-rank semisimple Lie groups on manifolds. We define two numbers r(G) and m(G) associated with the roots system of the Lie algebra of a Lie group G. If the dimension of the manifold is smaller than r(G), then we show the action preserves a Borel probability measure. If the dimension of the manifold is at most m(G), we show there is a quasi-invariant measure on the manifold such that the action is measurably isomorphic to a relatively measure-preserving action over a standard boundary action.