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The Kanenobu-Miyazawa conjecture and the Vassiliev-Gusarov skein modules based on mixed crossings


Authors: Józef H. Przytycki and Kouki Taniyama
Journal: Proc. Amer. Math. Soc. 129 (2001), 2799-2802
MSC (2000): Primary 57M27
DOI: https://doi.org/10.1090/S0002-9939-01-05854-3
Published electronically: February 9, 2001
MathSciNet review: 1838805
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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 [Enhancements On Off] (What's this?)

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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
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

DOI: https://doi.org/10.1090/S0002-9939-01-05854-3
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
Article copyright: © Copyright 2001 American Mathematical Society