The n-th root of a braid is unique up to conjugacy
classification
🧮 math.GT
math.GR
keywords
braidartinbraidsclassificationconjectureconjugacyconjugateelements
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We prove a conjecture due to Makanin: if a and b are elements of the Artin braid group B_n such that a^k=b^k for some nonzero integer k, then a and b are conjugate. The proof involves the Nielsen-Thurston classification of braids.
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