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arXiv · 1803.00866

Quasi-isometric embedding from the generalised Thompson's group $T_n$ to $T$

Xiaobing Sheng
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Abstract

Brown has defined the generalised Thompson's group $F_n$, $T_n$, where $n$ is an integer at least $2$ and Thompson's groups $F= F_2$ and $T =T_2$ in the 80's. Burillo, Cleary and Stein have found that there is a quasi-isometric embedding from $F_n$ to $F_m$ where $n$ and $m$ are positive integers at least 2. We show that there is a quasi-isometric embedding from $T_n$ to $T_2$ for any $n \geq 2$ and no embeddings from $T_2$ to $T_n$ for $n \geq 3$.

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BibTeXRIS

Xiaobing Sheng. 2021-06-29. Quasi-isometric embedding from the generalised Thompson's group $T_n$ to $T$. https://doi.org/10.3836/tjm%2F1502179371

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