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

Jözef H. Przytycki; Kouki Taniyama

doi:10.1090/s0002-9939-01-05854-3

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

Jözef H. Przytycki^*, Kouki Taniyama

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2799-2802
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	129
Issue number	9
DOIs	https://doi.org/10.1090/s0002-9939-01-05854-3
Publication status	Published - 2001
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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AB - 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.

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

Abstract

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