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Jones polynomials and classical conjectures in knot theory. II

  • Kunio Murasugi (a1)
Abstract

Let L be an alternating link and be its reduced (or proper) alternating diagram. Let w() denote the writhe of [3], i.e. the number of positive crossings minus the number of negative crossings. Let VL(t) be the Jones polynomial of L [2]. Let dmaxVL(t) and dminVL(t) denote the maximal and minimal degrees of VL(t), respectively. Furthermore, let σ(L) be the signature of L [5].

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[1] C. McA. Gordon and R. A. Litherland . On the signature of a link. Invent. Math. 47 (1978), 5369.

[5] K. Murasugi . On a certain numerical invariant of link types. Trans. Amer. Math. Soc. 117 (1965), 387422.

[6] K. Murasugi . Jones polynomials of alternating links. Trans. Amer. Math. Soc. 295 (1986), 147174.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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