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Proceedings of the American Mathematical Society

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Jones' braid-plat formula and a new surgery triple


Authors: Joan S. Birman and Taizo Kanenobu
Journal: Proc. Amer. Math. Soc. 102 (1988), 687-695
MSC: Primary 57M25
DOI: https://doi.org/10.1090/S0002-9939-1988-0929004-1
MathSciNet review: 929004
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Abstract: A link $ {L_\beta }\left( {2k,n - 2k} \right)$ is defined by a type $ \left( {2k,n - 2k} \right)$ pairing of an $ n$-braid $ \beta $ if the first $ 2k$ strands are joined up as in a plat and the remaining $ n - 2k$ as in a closed braid. The main result is a formula for the Jones polynomials of $ {L_\beta }\left( {2k,n - 2k} \right)$, valid for all $ k,0 \leqslant 2k \leqslant n$, which generalizes and relates earlier results of Jones for the cases $ n = 0$ and $ 2k$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0929004-1
Keywords: Jones polynomial, link, link diagram, braid, plat, orientation
Article copyright: © Copyright 1988 American Mathematical Society

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