Topology Seminar: An operad for splicing

I will describe a new operad (the "splicing operad") that acts on a fairly broad class of embedding spaces. Previously I constructed an action of the operad of little (j+1)-cubes on the space of framed long embeddings of R^j in R^n. This operad action can be seen an extension of the cubes action that allows for a general type of splicing operation. The space of long embeddings of R into R^3 was described as a free 2-cubes object over the subspace of prime long knots. With respect to the splicing operad, long knots in R^3 are again free, but rather than being free on the prime long knot subspace, the generating subspace is the (much smaller) torus and hyperbolic knot subspace. Moreover, the splicing operad has a particularly pleasant homotopy-type from the point of view of its structure maps.