ON THE CLASSIFICATION OF RATIONAL 3-TANGLES

Abstract

An n-string tangle (B3,T) is a 3-ball B3 containing n properly embedded arcs T={ti} and it is called rational if there is a homeomorphism of pairs from (B3,T) to (D,P)×I where D is the unit disk, P is any set of n points in the interior of D and I is the unit interval. In this article we partially generalize the well known classification of 2-string rational tangles to 3-string rational tangles. Using the results obtained we analyze knotted and linked products of site-specific recombination mediated by the Gin DNA invertase and give a possible solution to its action. Gin is an enzyme that carries out processive recombination.