Volume 7, issue 3 (2007)

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

Taizo Kanenobu

Algebraic & Geometric Topology 7 (2007) 1211–1232
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