纯辫群是RFRS
Pure braid groups are RFRS
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中文总结 AI 辅助
该研究证明纯辫群是RFRS，肯定了Agol2014年提出的辫群是否为虚拟RFRS的问题，还为Artin群是否虚拟特殊的问题提供了证据。
中文摘要 AI 辅助
Agol在其2014年ICM会议论文中提出问题11：辫群是否是（虚拟）RFRS。我们通过证明纯辫群是RFRS给出肯定回答。由此，多族Artin群为虚拟RFRS，包括A型$A_n$（辫群）、B型$B_n=C_n$、$\tilde A_n$及$\tilde C_n$。我们的结果也为辫群及更一般的Artin群是否虚拟特殊的问题提供了证据，参见文献[HagWi10的问题9.4]、[Wise14的问题13.4]。
英文摘要
Agol in his 2014 ICM proceedings article \cite[Question 11]{Agol14} asks whether braid groups are (virtually) RFRS. We answer this positively by showing that pure braid groups are RFRS. As a consequence, several families of Artin groups are virtually RFRS, including those of type $A_n$ (the braid groups), $B_n=C_n$, $\widetilde A_n$, and $\widetilde C_n$. Our results also provide evidence toward the problem of whether braid groups, and more generally Artin groups, are virtually special; see \cite[Problem 9.4]{HagWi10}, \cite[Problem 13.4]{Wise14}.
