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On the structure of the centralizer of a braid. (English) Zbl 1082.20024

For any given element of the \(n\)-string braid group, a small generating set of its centralizer is computed. This leads to sharp bounds for the size of a generating set for the centalizer, which is described in terms of semidirect and direct products of mixed braid groups. Nice figures and examples accompany the theorems. An explicit construction for the generating set is given.

MSC:

20F36 Braid groups; Artin groups
20F05 Generators, relations, and presentations of groups
20E07 Subgroup theorems; subgroup growth
57M25 Knots and links in the \(3\)-sphere (MSC2010)

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References:

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