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

Shengkui Ye

doi:10.1112/jlms.12260

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

Shengkui Ye^*

^*Corresponding author for this work

Department of Pure Mathematics

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

7 Citations (Scopus)

Abstract

We obtain a sufficient and necessary condition for a finite group to act effectively on a closed flat manifold. Let G = E_n(R), EU_n(R, Λ), SAut(F_n) or SOut(F_n). As applications, we prove that when n ≥ 3 every group action of G on a closed flat manifold M^k (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 language	English
Pages (from-to)	1065-1080
Number of pages	16
Journal	Journal of the London Mathematical Society
Volume	100
Issue number	3
DOIs	https://doi.org/10.1112/jlms.12260
Publication status	Published - 1 Dec 2019

Keywords

20F65
22F05
57S17 (primary)

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10.1112/jlms.12260

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AB - 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.

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KW - 57S17 (primary)

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ER -

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

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Keywords

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