TANGLE SOLUTIONS FOR COMPOSITE KNOTS: APPLICATION TO HIN RECOMBINATION

Abstract. We extend the tangle model, originally developed by Ernst and Sumners [18], to include com-posite knots. We show that, for any prime tangle, there are no rational tangle attachments of distance greater than one that first yield a 4-plat and then a connected sum of 4-plats. This is done by building on results on exceptional Dehn fillings at maximal distance. We then apply our results to the action of the Hin recombinase on mutated sites. In particular, after solving the tangle equations for processive recombi-nation, we use our work to give a complete set of solutions to the tangle equations modelling distributive recombination