Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-isometric embedding from the generalised Thompson's group $T_n$ to
  $T$   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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The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin