C1actions on manifolds by lattices in Lie groups

Aaron Brown; Danijela Damjanović; Zhiyuan Zhang

doi:10.1112/S0010437X22007278

C¹actions on manifolds by lattices in Lie groups

Aaron Brown, Danijela Damjanović, Zhiyuan Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

2 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 language	English (US)
Pages (from-to)	529-549
Number of pages	21
Journal	Compositio Mathematica
Volume	158
Issue number	3
DOIs	https://doi.org/10.1112/S0010437X22007278
State	Published - Mar 13 2022

Keywords

lattice actions
rigidity
Zimmer's conjecture

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1112/S0010437X22007278

Cite this

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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.",

keywords = "lattice actions, rigidity, Zimmer's conjecture",

author = "Aaron Brown and Danijela Damjanovi{\'c} and Zhiyuan Zhang",

note = "Funding Information: Brown was supported by NSF No.1752675. Damjanovi{\'c} was supported by Swedish Research Council grant VR2015-04644. Zhang was supported by the National Science Foundation under Grant No. DMS-1638352. Publisher Copyright: {\textcopyright} ",

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AU - Damjanović, Danijela

AU - Zhang, Zhiyuan

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PY - 2022/3/13

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N2 - 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.

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KW - rigidity

KW - Zimmer's conjecture

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