Characterization of Knots and Links Arising From Site-specific Recombination on Twist Knots

Details Characterization of Knots and Links Arising From Site-specific Recombination on Twist Knots Characterization of Knots and Links Arising From Site-specific Recombination on Twist Knots

2010-07-13

arxiv.org/abs/1007.2115v3

2011 J. Phys. A: Math. Theor. 44 045002

Mathematics

Geometric Topology

32 pages, 7 tables, 27 figures, revised: figures re-arranged, and minor corrections. To appear in Journal of Physics A

Scientific paper

We develop a model characterizing all possible knots and links arising from recombination starting with a twist knot substrate, extending previous work of Buck and Flapan. We show that all knot or link products fall into three well-understood families of knots and links, and prove that given a positive integer $n$, the number of product knots and links with minimal crossing number equal to $n$ grows proportionally to $n^5$. In the (common) case of twist knot substrates whose products have minimal crossing number one more than the substrate, we prove that the types of products are tightly prescribed. Finally, we give two simple examples to illustrate how this model can help determine previously uncharacterized experimental data.

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