On the actions of Higman-Thompson groups by homeomorphisms
Bull. Korean Math. Soc.
Published online August 20, 2019
Jinhong 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
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