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
- 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
Dedicated: In memory of Mikhail Gusarov (August 3, 1958 - June 25, 1999)