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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Slopes and colored Jones polynomials of adequate knots


Authors: David Futer, Efstratia Kalfagianni and Jessica S. Purcell
Journal: Proc. Amer. Math. Soc. 139 (2011), 1889-1896
MSC (2010): Primary 57M25, 57M27
Published electronically: 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.


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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: http://dx.doi.org/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
Published electronically: 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
Article copyright: © Copyright 2010 American Mathematical Society