Abstract
This paper extends the knot polynomial classification of DNA knots and catenanes, by incorporating a measure of supercoiling. Cozzarelli, Millett, and White have used the Jones polynomial and the generalised 2-variable polynomial to describe the products of iterated Tn3 resolvase recombination and phage λ integrase mediated recombination. A new polynomial invariant, Ω, is introduced; based on the regular isotopy invariants of Kauffman. The Ω polynomial is an invariant of framed links and involves the Whitney degree of the link. This is useful because it not only allows a regular isotopy classification, but also distinguishes between plectonemic and solenoidal supercoils. The enzymes above require plectonemic supercoils for the synaptic substrate, so we put the Ω polynomial to use to investigate the supercoiling of the recombination products.
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