TY - JOUR

T1 - Invariant measures and measurable projective factors for actions of higher-rank lattices on manifolds

AU - Brown, Aaron

AU - Hertz, Federico Rodriguez

AU - Wang, Zhiren

N1 - Publisher Copyright:
© 2022 Department of Mathematics, Princeton University.

PY - 2022/11

Y1 - 2022/11

N2 - 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.

AB - 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.

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U2 - 10.4007/annals.2022.196.3.2

DO - 10.4007/annals.2022.196.3.2

M3 - Article

AN - SCOPUS:85142218092

SN - 0003-486X

VL - 196

SP - 941

EP - 981

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 3

ER -