ON THE ACTIONS OF HIGMAN-THOMPSON GROUPS BY HOMEOMORPHISMS

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 wellknown 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

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Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

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