Zeros of the Jones Polynomial are Dense in the Complex Plane

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

Abstract


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.


Full Text: PDF