Braid groups are not profinitely rigid

2026/07/23 by Carl-Fredrik Nyberg-Brodda
#math.GR

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Abstract

We show that the n-strand braid group B_n is not profinitely rigid when n ≥ 4. We do this by exhibiting a family of pairwise non-isomorphic, finitely presented residually finite groups with the same profinite completion as 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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