Mathematics – Geometric Topology
Scientific paper
2007-07-26
Mathematics
Geometric Topology
18 pages, 3 tables, 18 figures. See also arXiv:0707.3775v1 for biological evidence for and applications of the model developed
Scientific paper
10.1088/1751-8113/40/41/008
We develop a topological model of knots and links arising from a single (or multiple processive) round(s) of recombination starting with an unknot, unlink, or (2,m)-torus knot or link substrate. We show that all knotted or linked products fall into a single family, and prove that the size of this family grows linearly with the cube of the minimum number of crossings. Additionally, we prove that the only possible products of an unknot substrate are either clasp knots and links or (2,m)-torus knots and links. Finally, in the (common) case of (2,m)-torus knot or link substrates whose products have minimal crossing number m+1, we prove that the types of products are tightly prescribed, and use this to examine previously uncharacterized experimental data.
Buck Dorothy
Flapan Erica
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