Matrix group actions on product of spheres

Shengkui Ye*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)729-747
Number of pages19
JournalJournal of Topology and Analysis
Volume14
Issue number3
DOIs
Publication statusPublished - 1 Sept 2022

Keywords

  • Zimmer's program
  • actions of linear groups

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