The Kauffman polynomial of periodic knots

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書誌事項

公開日
1993-04-01
DOI
  • 10.1016/0040-9383(93)90022-n
公開者
Elsevier BV

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説明

It is shown that the Kauffman 2-variable polynomial of a knot which is invariant under a rotation of odd prime period \(r\) about a disjoint axis satisfies strong congruences \(\text{mod}(r)\). It is observed in the introduction that the new criterion may be used to show that the knot \(10_{159}\) does not have such a symmetry of order 3. Most of the paper is algebraic, and is devoted to using the Birman-Wenzl-Murakami algebra [\textit{J. S. Birman} and \textit{H. Wenzl}, Trans. Am. Math. Soc. 313, 249- 273 (1989; Zbl 0684.57004); \textit{J. Murakami}, Publ. Res. Inst. Math. Sci. 26, 935-945 (1990; Zbl 0723.57006)] to describe the Kauffmann polynomials of torus knots and links and to obtain the main result for torus knots. The final section adapts arguments of \textit{P. Traczyk} [Invent. Math. 106, 73-84 (1991; Zbl 0753.57008)] to reduce the general case to the one already covered.

収録刊行物

  • Topology

    Topology 32 309-324, 1993-04-01

    Elsevier BV

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