Topology Seminar: Robin Koytcheff

Budney recently constructed an operad which encodes splicing of knots and proved a theorem decomposing the space of (long) knots over this operad. Infection of knots (or links) by string links is a generalization of splicing from knots to links and is useful for studying concordance of knots. In joint work with John Burke, we have constructed a colored operad that encodes this infection operation. This operad captures all the relations in the 2-string link monoid. We can also show that a certain subspace of 2-string links is freely generated over a suboperad of our infection colored operad by its subspace of prime links.