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

Primary: 57M25, 57M27

References

Publication

Received: 27 December 2005
Accepted: 26 July 2007
Published: 24 September 2007

Authors