用同胚论higman-thompson群的作用

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Korean Mathematical Society Pub Date : 2020-01-01 DOI:10.4134/BKMS.B190316

Jin Hong Kim

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引用次数: 0

摘要

本文的目的是通过同胚给出有限表示群作用的一些刚性结果。作为一个有趣的特例，我们证明了HigmanThompson群在具有非零欧拉特征的上同态流形上的作用是平凡的。这与著名的齐默程序有关，并表明同胚的作用可能与异胚的作用有很大的不同。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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ON THE ACTIONS OF HIGMAN-THOMPSON GROUPS BY HOMEOMORPHISMS

The aim of this short paper is to show some rigidity results for the actions of certain finitely presented groups by homeomorphisms. As an interesting and special case, we show that the actions of HigmanThompson groups by homeomorphisms on a cohomology manifold with a non-zero Euler characteristic should be trivial. This is related to the wellknown Zimmer program and shows that the actions by homeomorphism could be very much different from those by diffeomorphisms.

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来源期刊

Bulletin of the Korean Mathematical Society 数学-数学

CiteScore

0.80

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).