Zeros of the Jones Polynomial are Dense in the Complex Plane

  • Xian'an Jin
  • Fuji Zhang
  • Fengming Dong
  • Eng Guan Tay


In this paper, we present a formula for computing the Tutte polynomial of the signed graph formed from a labeled graph by edge replacements in terms of the chain polynomial of the labeled graph. Then we define a family of 'ring of tangles' links and consider zeros of their Jones polynomials. By applying the formula obtained, Beraha-Kahane-Weiss's theorem and Sokal's lemma, we prove that zeros of Jones polynomials of (pretzel) links are dense in the whole complex plane.

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