C1actions on manifolds by lattices in Lie groups

Aaron Brown, Danijela Damjanović, Zhiyuan Zhang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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
Volume158
Issue number3
DOIs
StatePublished - Mar 13 2022

Funding

Brown was supported by NSF No.1752675. Damjanović was supported by Swedish Research Council grant VR2015-04644. Zhang was supported by the National Science Foundation under Grant No. DMS-1638352.

Keywords

  • Zimmer's conjecture
  • lattice actions
  • rigidity

ASJC Scopus subject areas

  • Algebra and Number Theory

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