## Topology Seminar: An operad for splicing

- Date: 03/03/2010

University of British Columbia

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.

4:00 - 5:00pm, WMAX 110.