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

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 ou...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2001-09, Vol.129 (9), p.2799-2802
Main Authors: Przytycki, Józef H., Taniyama, Kouki
Format: Article
Language:English
Subjects:
College mathematics
Mathematical theorems
Mathematics
Myeloma proteins
Polynomials
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-01-05854-3