• Title/Summary/Keyword: periodic link with rational quotient

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A RECURSIVE FORMULA FOR THE JONES POLYNOMIAL OF 2-BRIDGE LINKS AND APPLICATIONS

  • Lee, Eun-Ju;Lee, Sang-Youl;Seo, Myoung-Soo
    • Journal of the Korean Mathematical Society
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    • v.46 no.5
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    • pp.919-947
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    • 2009
  • In this paper, we give a recursive formula for the Jones polynomial of a 2-bridge knot or link with Conway normal form C($-2n_1$, $2n_2$, $-2n_3$, ..., $(-1)_r2n_r$) in terms of $n_1$, $n_2$, ..., $n_r$. As applications, we also give a recursive formula for the Jones polynomial of a 3-periodic link $L^{(3)}$ with rational quotient L = C(2, $n_1$, -2, $n_2$, ..., $n_r$, $(-1)^r2$) for any nonzero integers $n_1$, $n_2$, ..., $n_r$ and give a formula for the span of the Jones polynomial of $L^{(3)}$ in terms of $n_1$, $n_2$, ..., $n_r$ with $n_i{\neq}{\pm}1$ for all i=1, 2, ..., r.