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Transactions of the American Mathematical Society

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Twist regions and coefficients stability of the colored Jones polynomial


Authors: Mohamed Elhamdadi, Mustafa Hajij and Masahico Saito
Journal: Trans. Amer. Math. Soc. 370 (2018), 5155-5177
MSC (2010): Primary 57M27
DOI: https://doi.org/10.1090/tran/7128
Published electronically: February 8, 2018
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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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Additional Information

Mohamed Elhamdadi
Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33647
Email: emohamed@mail.usf.edu

Mustafa Hajij
Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33647
Address at time of publication: Department of Computer Science and Engineering, University of South Florida, Tampa, Florida 33647
Email: mhajij@usf.edu

Masahico Saito
Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33647
Email: saito@usf.edu

DOI: https://doi.org/10.1090/tran/7128
Received by editor(s): August 3, 2016
Received by editor(s) in revised form: November 14, 2016
Published electronically: February 8, 2018
Article copyright: © Copyright 2018 American Mathematical Society

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