A colored operad for string link infection

Abstract

Budney recently constructed an operad that encodes splicing of knots. He further showed that the space of (long) knots is generated over this operad by the space of torus knots and hyperbolic knots, thus generalizing the satellite decomposition of knots from isotopy classes to the level of the space of knots. Infection by string links is a generalization of splicing from knots to links. We construct a colored operad that encodes string link infection. We prove that a certain subspace of the space of 2-component string links is generated over a suboperad of our operad by its subspace of prime links. This generalizes a result from joint work with Blair from isotopy classes of knots to the space of knots. Furthermore, all the relations in the monoid of 2-string links (as determined in our joint work with Blair) are captured by our infection operad.