A relationship between the Jones and Kauffman polynomials

King, Christopher

doi:10.1090/S0002-9947-1992-1034666-2

A relationship between the Jones and Kauffman polynomials
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Trans. Amer. Math. Soc. 329 (1992), 307-323 Request permission

Abstract:

A simple relationship is presented between the Kauffman polynomial of a framed link $L$ and the Jones polynomial of a derived link $\tilde L$. The link is $\tilde L$ obtained by splitting each component of $L$ into two parallel strands, using the framing to determine the linking number of the strands. The relation is checked in several nontrivial examples, and a proof of the general result is given.

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