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

Aaron Brown*, Federico Rodriguez Hertz, Zhiren Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)941-981
Number of pages41
JournalAnnals of Mathematics
Volume196
Issue number3
DOIs
StatePublished - Nov 2022

Keywords

  • Invariant measures
  • Lattice actions
  • Lyapunov exponents
  • Zimmer program

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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