Twist regions and coefficients stability of the colored Jones polynomial

Elhamdadi, Mohamed; Hajij, Mustafa; Saito, Masahico

doi:10.1090/tran/7128

Twist regions and coefficients stability of the colored Jones polynomial
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by Mohamed Elhamdadi, Mustafa Hajij and Masahico Saito PDF

Trans. Amer. Math. Soc. 370 (2018), 5155-5177 Request permission

Abstract:

We prove that the coefficients of the colored Jones polynomial of alternating links stabilize under increasing the number of twists in the twist regions of the link diagram. This gives us an infinite family of $q$-power series derived from the colored Jones polynomial parametrized by the color and the twist regions of the alternating link diagram.

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