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

Kanenobu, Taizo

doi:10.2140/agt.2007.7.1211

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

Taizo Kanenobu

Algebraic & Geometric Topology 7 (2007) 1211–1232

DOI: 10.2140/agt.2007.7.1211

Abstract

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.

Keywords

HOMFLYPT polynomial, two-cable link, skein relation

Mathematical Subject Classification 2000

Primary: 57M25, 57M27

References

Publication

Received: 27 December 2005

Accepted: 26 July 2007

Published: 24 September 2007

Authors

Taizo Kanenobu
Department of Mathematics Osaka City University Sugimoto Sumiyoshi-ku Osaka 558-8585 Japan

Volume 7, issue 3 (2007)