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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 101, Issue 2
  • March 1987, pp. 267-278

The 2-variable polynomial of cable knots

  • H. R. Morton (a1) and H. B. Short (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100066627
  • Published online: 24 October 2008
Abstract
Abstract

The 2-variable polynomial PK of a satellite K is shown not to satisfy any formula, relating it to the polynomial of its companion and of the pattern, which is at all similar to the formulae for Alexander polynomials. Examples are given of various pairs of knots which can be distinguished by calculating P for 2-strand cables about them even though the knots themselves share the same P. Properties of a given knot such as braid index and amphicheirality, which may not be apparent from the knot's polynomial P, are shown in certain cases to be detectable from the polynomial of a 2-cable about the knot.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]J. S. Birman , On the Jones polynomial of closed 3-braids. Invent. Math 81 (1985), 287294.

[2]R. H. Fox . Free differential calculus V. The Alexander matrices re-examined. Ann. Math. 71 (1960), 408422.

[5]P. Freyd , D. Yetter , J. Hoste , W. B. R. Lickorish , K. C. Millett and A. Ocneanu , A new polynomial invariant of knots and links. Bull. Amer. Math. Soc. 12 (1985), 239246.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
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