Symmetries of flat manifolds, Jordan property and the general Zimmer program

Shengkui Ye*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


We obtain a sufficient and necessary condition for a finite group to act effectively on a closed flat manifold. Let G = En(R), EUn(R, Λ), SAut(Fn) or SOut(Fn). As applications, we prove that when n ≥ 3 every group action of G on a closed flat manifold Mk (k < n) by homeomorphisms is trivial. This confirms a conjecture related to Zimmer's program for flat manifolds. Moreover, it is also proved that the group of homeomorphisms of closed flat manifolds are Jordan with Jordan constants depending only on dimensions.

Original languageEnglish
Pages (from-to)1065-1080
Number of pages16
JournalJournal of the London Mathematical Society
Issue number3
Publication statusPublished - 1 Dec 2019


  • 20F65
  • 22F05
  • 57S17 (primary)


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