The head and tail of the colored Jones polynomial for adequate knots
HTML articles powered by AMS MathViewer
- by Cody Armond and Oliver T. Dasbach PDF
- Proc. Amer. Math. Soc. 145 (2017), 1357-1367 Request permission
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.References
- Cody Armond and Oliver T. Dasbach, Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial, arXiv:1106.3948 (2011), 1–27.
- Cody Armond, The head and tail conjecture for alternating knots, Algebr. Geom. Topol. 13 (2013), no. 5, 2809–2826. MR 3116304, DOI 10.2140/agt.2013.13.2809
- Cody W. Armond, Walks along braids and the colored Jones polynomial, J. Knot Theory Ramifications 23 (2014), no. 2, 1450007, 15. MR 3197051, DOI 10.1142/S0218216514500072
- Dror Bar-Natan, KnotTheory, http://katlas.org, 2011.
- Oliver T. Dasbach and Xiao-Song Lin, On the head and the tail of the colored Jones polynomial, Compos. Math. 142 (2006), no. 5, 1332–1342. MR 2264669, DOI 10.1112/S0010437X06002296
- Oliver T. Dasbach and Xiao-Song Lin, A volumish theorem for the Jones polynomial of alternating knots, Pacific J. Math. 231 (2007), no. 2, 279–291. MR 2346497, DOI 10.2140/pjm.2007.231.279
- Oliver Dasbach and Anastasiia Tsvietkova, A refined upper bound for the hyperbolic volume of alternating links and the colored Jones polynomial, Math. Res. Lett. 22 (2015), no. 4, 1047–1060. MR 3391876, DOI 10.4310/MRL.2015.v22.n4.a5
- David Futer, Efstratia Kalfagianni, and Jessica S. Purcell, Dehn filling, volume, and the Jones polynomial, J. Differential Geom. 78 (2008), no. 3, 429–464. MR 2396249
- David Futer, Efstratia Kalfagianni, and Jessica S. Purcell, Guts of surfaces and the colored Jones polynomial, Lecture Notes in Mathematics, vol. 2069, Springer, Heidelberg, 2013.
- David Futer, Fiber detection for state surfaces, Algebr. Geom. Topol. 13 (2013), no. 5, 2799–2807. MR 3116303, DOI 10.2140/agt.2013.13.2799
- Stavros Garoufalidis and Thang T. Q. Lê, Nahm sums, stability and the colored Jones polynomial, Res. Math. Sci. 2 (2015), Art. 1, 55. MR 3375651, DOI 10.1186/2197-9847-2-1
- W. B. Raymond Lickorish, An introduction to knot theory, Graduate Texts in Mathematics, vol. 175, Springer-Verlag, New York, 1997. MR 1472978, DOI 10.1007/978-1-4612-0691-0
- G. Masbaum and P. Vogel, $3$-valent graphs and the Kauffman bracket, Pacific J. Math. 164 (1994), no. 2, 361–381. MR 1272656, DOI 10.2140/pjm.1994.164.361
- Lev Rozansky, Khovanov homology of a unicolored B-adequate link has a tail, Quantum Topol. 5 (2014), no. 4, 541–579. MR 3317343, DOI 10.4171/QT/58
- Alexander Stoimenow and Toshifumi Tanaka, Mutation and the colored Jones polynomial, J. Gökova Geom. Topol. GGT 3 (2009), 44–78. MR 2595755
Additional Information
- Cody Armond
- Affiliation: Department of Mathematics, Ohio State University at Mansfield, 1760 University Drive, Mansfield, Ohio 44906
- MR Author ID: 1039228
- Email: armond.2@osu.edu
- Oliver T. Dasbach
- Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
- MR Author ID: 612149
- Email: kasten@math.lsu.edu
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 1357-1367
- MSC (2010): Primary 57M27
- DOI: https://doi.org/10.1090/proc/13211
- MathSciNet review: 3589331