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arXiv · 2101.09928

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

Motoko Kato
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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.

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Motoko Kato. 2021-01-25. Semi-simple actions of the Higman-Thompson groups $T_n$ on finite-dimensional CAT(0) spaces. https://doi.org/10.1007/s10711-023-00826-7

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