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Slopes and colored Jones polynomials of adequate knots
Author(s):
David
Futer;
Efstratia
Kalfagianni;
Jessica
S.
Purcell
Journal:
Proc. Amer. Math. Soc.
139
(2011),
1889-1896.
MSC (2010):
Primary 57M25, 57M27
Posted:
October 29, 2010
MathSciNet review:
2763776
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Abstract:
Garoufalidis conjectured a relation between the boundary slopes of a knot and its colored Jones polynomials. According to the conjecture, certain boundary slopes are detected by the sequence of degrees of the colored Jones polynomials. We verify this conjecture for adequate knots, a class that vastly generalizes that of alternating knots.
References:
-
- 1.
- Cynthia L. Curtis and Samuel Taylor, The Jones polynomial and boundary slopes of alternating knots, arXiv:0910.4912.
- 2.
- Oliver T. Dasbach, David Futer, Efstratia Kalfagianni, Xiao-Song Lin, and Neal W. Stoltzfus, The Jones polynomial and graphs on surfaces, Journal of Combinatorial Theory Ser. B 98 (2008), no. 2, 384-399. MR 2389605 (2009d:57020)
- 3.
- Nathan M. Dunfield, A table of boundary slopes of Montesinos knots, Topology 40 (2001), no. 2, 309-315. MR 1808223 (2001j:57008)
- 4.
- David Futer, Efstratia Kalfagianni, and Jessica S. Purcell, Guts of surfaces and the colored Jones polynomial, in preparation.
- 5.
- -, Symmetric links and Conway sums: volume and Jones polynomial, Math. Res. Lett. 16 (2009), no. 2, 233-253. MR 2496741
- 6.
- Stavros Garoufalidis, The Jones slopes of a knot, arXiv:0911.3627, Journal of Quantum Topology, to appear.
- 7.
- Allen E. Hatcher, On the boundary curves of incompressible surfaces, Pacific J. Math. 99 (1982), no. 2, 373-377. MR 658066 (83h:57016)
- 8.
- Allen E. Hatcher and Ulrich Oertel, Boundary slopes for Montesinos knots, Topology 28 (1989), no. 4, 453-480. MR 1030987 (91e:57016)
- 9.
- W. B. Raymond Lickorish, An introduction to knot theory, Graduate Texts in Mathematics, vol. 175, Springer-Verlag, New York, 1997. MR 1472978 (98f:57015)
- 10.
- W. B. Raymond Lickorish and Morwen B. Thistlethwaite, Some links with nontrivial polynomials and their crossing-numbers, Comment. Math. Helv. 63 (1988), no. 4, 527-539. MR 966948 (90a:57010)
- 11.
- Makoto Ozawa, Essential state surfaces for adequate knots and links, arXiv:0609166, Journal of the Australian Mathematical Society, to appear.
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Additional Information:
David
Futer
Affiliation:
Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
Email:
dfuter@temple.edu
Efstratia
Kalfagianni
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email:
kalfagia@math.msu.edu
Jessica
S.
Purcell
Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email:
jpurcell@math.byu.edu
DOI:
10.1090/S0002-9939-2010-10617-2
PII:
S 0002-9939(2010)10617-2
Received by editor(s):
February 8, 2010
Received by editor(s) in revised form:
May 25, 2010
Posted:
October 29, 2010
Additional Notes:
The first author is supported in part by NSF grant DMS-1007221
The second author is supported in part by NSF grant DMS–0805942
The third author is supported in part by NSF grant DMS–0704359
Communicated by:
Daniel Ruberman
Copyright of article:
Copyright
2010,
American Mathematical Society
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