Semi-simple actions of the Higman-Thompson groups T_n on finite-dimensional CAT(0) spaces

Abstract

In this paper, we study isometric actions on finite-dimensional CAT(0) spaces for the Higman–Thompson groups T_n, which are generalizations of Thompson’s group T. It is known that every semi-simple action of T on a complete CAT(0) space of finite covering dimension has a global fixed point. After this result, we show that every semi-simple action of T_n on a complete CAT(0) space of finite covering dimension has a global fixed point. In the proof, we regard T_n as ring groups of homeomorphisms of S^1 introduced by Kim, Koberda and Lodha, and use general facts on these groups.