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arXiv · 2607.20859

Braid groups are not profinitely rigid

Carl-Fredrik Nyberg-Brodda
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Abstract

We show that the $n$-strand braid group $\mathbf{B}_n$ is not profinitely rigid when $n \geq 4$. We do this by exhibiting a family of pairwise non-isomorphic, finitely presented residually finite groups with the same profinite completion as $\mathbf{B}_n$. This answers a well-known problem negatively, and gives the first known examples of non-profinitely rigid mapping class groups.

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Carl-Fredrik Nyberg-Brodda. 2026-07-23. Braid groups are not profinitely rigid. https://arxiv.org/abs/2607.20859

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