The \(n\)th root of a braid is unique up to conjugacy. (Q1880607)
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| Language | Label | Description | Also known as |
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| English | The \(n\)th root of a braid is unique up to conjugacy. |
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The \(n\)th root of a braid is unique up to conjugacy. (English)
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30 September 2004
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The author proves a conjecture due to Makanin: if \(\alpha\) and \(\beta\) are elements of the Artin braid group \(B_n\) such that \(\alpha^k=\beta^k\) for some nonzero integer \(k\), then \(\alpha\) and \(\beta\) are conjugate. The proof involves the Nielsen-Thurston classification of braids.
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braid groups
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unique roots
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conjugacy
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Nielsen-Thurston theory
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