Bulletin of the
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BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2020; 57(2): 449-457

Online first article December 24, 2019      Printed March 31, 2020

https://doi.org/10.4134/BKMS.b190316

Copyright © The Korean Mathematical Society.

On the actions of Higman-Thompson groups by homeomorphisms

Jin Hong Kim

Chosun University

Abstract

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 Higman-Thompson groups by homeomorphisms on a cohomology manifold with a non-zero Euler characteristic should be trivial. This is related to the well-known Zimmer program and shows that the actions by homeomorphism could be very much different from those by diffeomorphisms.

Keywords: Higman-Thompson groups, finitely presented infinite simple groups, finite abelian groups, cohomology manifolds, Zimmer program

MSC numbers: 20F65, 20F28, 57S25

Supported by: This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1B03930639, 2019R1F1A1041025)

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