Pure braid groups are RFRS

Xiaolei Wu; Shengkui Ye

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arXiv · 2608.13978

Pure braid groups are RFRS

Xiaolei Wu·Shengkui Ye

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Abstract

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}.

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BibTeX RIS

Xiaolei Wu, Shengkui Ye. 2026-08-14. Pure braid groups are RFRS. https://arxiv.org/abs/2608.13978

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