A formula for the braid index of links |
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Authors: | Sang Youl Lee Myoungsoo Seo |
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Affiliation: | aDepartment of Mathematics, Pusan National University, Pusan 609-735, Republic of Korea;bDepartment of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea |
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Abstract: | Morton and Franks–Williams independently gave a lower bound for the braid index b(L) of a link L in S3 in terms of the v-span of the Homfly-pt polynomial PL(v,z) of L: . Up to now, many classes of knots and links satisfying the equality of this Morton–Franks–Williams's inequality have been founded. In this paper, we give a new such a class of knots and links and make an explicit formula for determining the braid index of knots and links that belong to the class . This gives simultaneously a new class of knots and links satisfying the Jones conjecture which says that the algebraic crossing number in a minimal braid representation is a link invariant. We also give an algorithm to find a minimal braid representative for a given knot or link in . |
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Keywords: | Braid index Index of a graph Homfly-pt polynomial Minimal braid representation MFW inequality |
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