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.