论文标题
希格曼 - 汤普森小组的非界限
Non-inner amenability of the Higman-Thompson groups
论文作者
论文摘要
我们证明，Higman-Thompson组$ t_n $和$ v_n $对于所有$ n \ ge 2 $都不适合。这扩展了Haagerup和Olesen的结果，即Thompson的组$ t = t_2 $和$ v = v_2 $是不可行的。他们的证明仅在$ n = 2 $ case中可用，即瑟斯顿（Thurston）的汤普森（Thompson）组$ t $的分段项目模型，因此我们的方法必然使用不同的工具。当$ n = 2 $时，这也提供了Haagerup-Ouser的结果的替代证明。
We prove that the Higman-Thompson groups $T_n$ and $V_n$ are non-inner amenable for all $n\ge 2$. This extends Haagerup and Olesen's result that Thompson's groups $T=T_2$ and $V=V_2$ are non-inner amenable. Their proof relied on machinery only available in the $n=2$ case, namely Thurston's piecewise-projective model for Thompson's group $T$, so our approach necessarily utilizes different tools. This also provides an alternate proof of Haagerup-Olesen's result when $n=2$.
