Twist regions and coefficients stability of the colored Jones polynomial

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 qq-power series derived from the colored Jones polynomial parametrized by the color and th...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2018-07, Vol.370 (7), p.5155-5177
Main Authors: Elhamdadi, Mohamed, Hajij, Mustafa, Saito, Masahico
Format: Article
Language:English
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Research article
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Summary: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 qq-power series derived from the colored Jones polynomial parametrized by the color and the twist regions of the alternating link diagram.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/7128