Abstract
AbstractIn this paper, we study isometric actions on finite-dimensional CAT(0) spaces for the Higman–Thompson groups $$T_n$$
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 $$T_n$$
T
n
on a complete CAT(0) space of finite covering dimension has a global fixed point. In the proof, we regard $$T_n$$
T
n
as ring groups of homeomorphisms of $$S^1$$
S
1
introduced by Kim, Koberda and Lodha, and use general facts on these groups.
Funder
Japan Society for the Promotion of Science
ACT-X, Japan Science and Technology Agency
Publisher
Springer Science and Business Media LLC
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