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The head and tail of the colored Jones polynomial for adequate knots


Authors: Cody Armond and Oliver T. Dasbach
Journal: Proc. Amer. Math. Soc. 145 (2017), 1357-1367
MSC (2010): Primary 57M27
DOI: https://doi.org/10.1090/proc/13211
Published electronically: October 24, 2016
MathSciNet review: 3589331
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Abstract: We show that the head and tail functions of the colored Jones polynomial of adequate links are the product of head and tail functions of the colored Jones polynomial of alternating links that can be read-off an adequate diagram of the link. We apply this to strengthen a theorem of Kalfagianni, Futer and Purcell on the fiberedness of adequate links.


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Additional Information

Cody Armond
Affiliation: Department of Mathematics, Ohio State University at Mansfield, 1760 University Drive, Mansfield, Ohio 44906
Email: armond.2@osu.edu

Oliver T. Dasbach
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: kasten@math.lsu.edu

DOI: https://doi.org/10.1090/proc/13211
Received by editor(s): March 21, 2014
Received by editor(s) in revised form: March 21, 2016, and March 22, 2016
Published electronically: October 24, 2016
Additional Notes: The first author was partially supported as a graduate student by NSF VIGRE grant DMS 0739382.
The second author was supported in part by NSF grant DMS-1317942
Communicated by: Martin Scharlemann
Article copyright: © Copyright 2016 American Mathematical Society