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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Slopes and colored Jones polynomials of adequate knots
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by David Futer, Efstratia Kalfagianni and Jessica S. Purcell PDF
Proc. Amer. Math. Soc. 139 (2011), 1889-1896 Request permission

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
  • MR Author ID: 671567
  • ORCID: 0000-0002-2595-6274
  • 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
  • MR Author ID: 807518
  • ORCID: 0000-0002-0618-2840
  • Email: jpurcell@math.byu.edu
  • 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
  • © Copyright 2010 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 1889-1896
  • MSC (2010): Primary 57M25, 57M27
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10617-2
  • MathSciNet review: 2763776