A skein relation for the HOMFLYPT polynomials of two-cable links

Kanenobu, Taizo¹

¹Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

Algebraic and Geometric Topology, Tome 7 (2007) no. 3, pp. 1211-1232

Résumé

We give a skein relation for the HOMFLYPT polynomials of 2–cable links. We have constructed arbitrarily many 2–bridge knots sharing the same HOMFLYPT, Kauffman, and Links–Gould polynomials, and arbitrarily many 2–bridge links sharing the same HOMFLYPT, Kauffman, Links–Gould, and 2–variable Alexander polynomials. Using the skein relation, we show their 2–cable links also share the same HOMFLYPT polynomials.

Détail

DOI : 10.2140/agt.2007.7.1211

Keywords: HOMFLYPT polynomial, two-cable link, skein relation

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