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A relationship between the Jones and Kauffman polynomials

Author: Christopher King
Journal: Trans. Amer. Math. Soc. 329 (1992), 307-323
MSC: Primary 57M25
MathSciNet review: 1034666
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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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