Matrix group actions on product of spheres

Shengkui Ye

doi:10.1142/S1793525321500072

Matrix group actions on product of spheres

Shengkui Ye^*

^*Corresponding author for this work

Department of Pure Mathematics

NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai

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

Abstract

Let SLn(a) be the special linear group over integers and Mr = Sr1 Sr2, Tr1 Sr2, or Tr0 Sr1 Sr2, products of spheres and tori. We prove that any group action of SLn(a;) on Mr by diffeomorphims or piecewise linear homeomorphisms is trivial if r < n - 1. This confirms a conjecture on Zimmer's program for these manifolds.

Original language	English
Pages (from-to)	729-747
Number of pages	19
Journal	Journal of Topology and Analysis
Volume	14
Issue number	3
DOIs	https://doi.org/10.1142/S1793525321500072
Publication status	Published - 1 Sept 2022

Keywords

Zimmer's program
actions of linear groups

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10.1142/S1793525321500072

Cite this

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title = "Matrix group actions on product of spheres",

abstract = "Let SLn(a) be the special linear group over integers and Mr = Sr1 Sr2, Tr1 Sr2, or Tr0 Sr1 Sr2, products of spheres and tori. We prove that any group action of SLn(a;) on Mr by diffeomorphims or piecewise linear homeomorphisms is trivial if r < n - 1. This confirms a conjecture on Zimmer's program for these manifolds.",

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N2 - Let SLn(a) be the special linear group over integers and Mr = Sr1 Sr2, Tr1 Sr2, or Tr0 Sr1 Sr2, products of spheres and tori. We prove that any group action of SLn(a;) on Mr by diffeomorphims or piecewise linear homeomorphisms is trivial if r < n - 1. This confirms a conjecture on Zimmer's program for these manifolds.

AB - Let SLn(a) be the special linear group over integers and Mr = Sr1 Sr2, Tr1 Sr2, or Tr0 Sr1 Sr2, products of spheres and tori. We prove that any group action of SLn(a;) on Mr by diffeomorphims or piecewise linear homeomorphisms is trivial if r < n - 1. This confirms a conjecture on Zimmer's program for these manifolds.

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KW - actions of linear groups

UR - https://www.scopus.com/pages/publications/85096542488

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DO - 10.1142/S1793525321500072

M3 - Article

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JO - Journal of Topology and Analysis

JF - Journal of Topology and Analysis

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Matrix group actions on product of spheres

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