Untangling DNA. (English) Zbl 0712.57002

“Knot theory - a new kind of applicable mathematics!” This starts an excellent survey article which provides the reader with a glimpse of a topological approach to enzymology, the geometry of DNA, site-specific recombination, tangles and 4-plats, Tn3 resolvase, and Phage \(\lambda\) Integrase. Resolvase recombinations lead to tangle equations and it is shown how the Cyclic Surgery Theorem of Culler, Gordon, Luecke-Shalen and the Determination of Knots by their Complements Theorem of Gordon-Luecke can be used to solve certain such tangle equations for the tangle factors. The author rightfully concludes the article with the hope that he has provided the reader with some reason to question a statement of Cipra [Science 241, 1291-1292 (1988)]: “Gordon and Luecke’s solution to Tietze’s 80 year-old problem has no immediate practical or even theoretical applications.”
Reviewer: W.Heil


57M25 Knots and links in the \(3\)-sphere (MSC2010)
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
92C40 Biochemistry, molecular biology
Full Text: DOI


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