球积上的矩阵群作用

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Topology and Analysis Pub Date : 2020-11-16 DOI:10.1142/s1793525321500072

Shengkui Ye

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引用次数: 0

摘要

设[公式:见文]为整数和[公式:见文][公式:见文][公式:见文]，或[公式:见文]球面和环面之积的特殊线性群。我们证明了[公式:见文]在[公式:见文]上的任何由微分同态或分段线性同胚引起的群作用是平凡的，如果[公式:见文]，这证实了关于这些流形的齐默规划的一个猜想。

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Matrix group actions on product of spheres

Let [Formula: see text] be the special linear group over integers and [Formula: see text] [Formula: see text], or [Formula: see text] products of spheres and tori. We prove that any group action of [Formula: see text] on [Formula: see text] by diffeomorphims or piecewise linear homeomorphisms is trivial if [Formula: see text] This confirms a conjecture on Zimmer’s program for these manifolds.

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来源期刊

Journal of Topology and Analysis MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is devoted to topology and analysis, broadly defined to include, for instance, differential geometry, geometric topology, geometric analysis, geometric group theory, index theory, noncommutative geometry, and aspects of probability on discrete structures, and geometry of Banach spaces. We welcome all excellent papers that have a geometric and/or analytic flavor that fosters the interactions between these fields. Papers published in this journal should break new ground or represent definitive progress on problems of current interest. On rare occasion, we will also accept survey papers.