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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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The Kanenobu-Miyazawa conjecture and the Vassiliev-Gusarov skein modules based on mixed crossings
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by Józef H. Przytycki and Kouki Taniyama PDF
Proc. Amer. Math. Soc. 129 (2001), 2799-2802 Request permission

Abstract:

We show that a Brunnian link of $n$ components and the $n$ component trivial link share the same first $n-1$ coefficients of the Jones-Conway (Homflypt) polynomial (answering the question of Kanenobu and Miyazawa). We prove also the similar result for the Kauffman polynomial of Brunnian links. We place our solution in the context of Vassiliev-Gusarov skein modules based on mixed singular crossings.
References
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Additional Information
  • Józef H. Przytycki
  • Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742; Department of Mathematics, George Washington University, Washington, DC 20052
  • MR Author ID: 142495
  • Email: przytyck@gwu.edu
  • Kouki Taniyama
  • Affiliation: Department of Mathematics, Tokyo Woman’s Christian University, Zempukuji, Suginamiku, Tokyo, 167-8585, Japan
  • Email: taniyama@twcu.ac.jp
  • Received by editor(s): August 24, 1999
  • Received by editor(s) in revised form: January 14, 2000
  • Published electronically: February 9, 2001
  • Additional Notes: The first author was partially supported by NSF grant DMS-9808955

    • Dedicated: In memory of Mikhail Gusarov (August 3, 1958 - June 25, 1999)
  • Communicated by: Ronald Fintushel
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 2799-2802
  • MSC (2000): Primary 57M27
  • DOI: https://doi.org/10.1090/S0002-9939-01-05854-3
  • MathSciNet review: 1838805