On the actions of Higman-Thompson groups by homeomorphisms
Bull. Korean Math. Soc. 2020 Vol. 57, No. 2, 449-457
https://doi.org/10.4134/BKMS.b190316
Published online December 24, 2019
Printed March 31, 2020
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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