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Abstract commensurators of braid groups. (English) Zbl 1103.20034
Summary: Let \(B_n\) be the braid group on \(n\geqslant 4\) strands. We show that the abstract commensurator of \(B_n\) is isomorphic to \(\text{Mod}(S)\ltimes(\mathbb{Q}^\times\ltimes\mathbb{Q}^\infty)\), where \(\text{Mod}(S)\) is the extended mapping class group of the sphere with \(n+1\) punctures.

MSC:
20F36 Braid groups; Artin groups
20F34 Fundamental groups and their automorphisms (group-theoretic aspects)
57M07 Topological methods in group theory
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