Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A RECURSIVE FORMULA FOR THE JONES POLYNOMIAL OF 2-BRIDGE LINKS AND APPLICATIONS

  • Lee, Eun-Ju (DEPARTMENT OF MATHEMATICS GRADUATE SCHOOL OF NATURAL SCIENCES PUSAN NATIONAL UNIVERSITY) ;
  • Lee, Sang-Youl (DEPARTMENT OF MATHEMATICS PUSAN NATIONAL UNIVERSITY) ;
  • Seo, Myoung-Soo (DEPARTMENT OF MATHEMATICS KYUNGPOOK NATIONAL UNIVERSITY)
  • Published : 2009.09.01
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Abstract

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.

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References

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