C1actions on manifolds by lattices in Lie groups

Aaron Brown, Danijela Damjanović, Zhiyuan Zhang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In this paper we study Zimmer's conjecture for actions of lattice subgroup of a higher-rank simple Lie group with finite center on compact manifolds.We show that when the rank of an uniform lattice is larger than the dimension of the manifold, then the action factors through a finite group.For lattices in, the dimensional bound is sharp.

Original languageEnglish (US)
Pages (from-to)529-549
Number of pages21
JournalCompositio Mathematica
Issue number3
StatePublished - Mar 13 2022


  • Zimmer's conjecture
  • lattice actions
  • rigidity

ASJC Scopus subject areas

  • Algebra and Number Theory


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