The tangle model for composite knots, with applications to DNA recombination

speaker: Mauro Mauricio (Imperial College London)

abstract: The tangle model, developed by Ernst and Sumners and the late 1980s, had remarkable success in illuminating the topology of DNA interactions resulting from processive recombination. However, the scope of the model was limited to DNA konts belonging to the family of 4-plats. There are situations, such as distributive recombination mediated by the Hin protein, where composite knot products (these are never 4-plats) are formed. In this talk, we show how to extend the tangle analysis to deal with products which are composite knots. Mathematically, we extend the results of Boyer and Zhang on exceptional Dehn fillings at maximal distance and prove (in particular) that if a rational tangle replacement (whose complement is a prime tangle) on a 4-plat yields a connect sum of 4-plats, then the distance between the rational tangles must be less than or equal to 1.

We conjecture that, if both the substrate and the product share a common non-trivial summand, then this is impossible (for prime tangles), and so the only way to obtain connect sums of 4-plats from rational tangle replacement on a 4-plat under these assumptions is the obvious one. This would have implications for distributive Hin-mediated recombination. We conclude by mentioning an on-going program to prove this conjecture, using Heegaard Floer homology, together with examples supporting our claim.

timetable:
Wed 15 Jun, 17:00 - 17:45, Aula Dini
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