Topology Seminar: An operad for splicing

  • Date: 03/03/2010
Ryan Budney (University of Victoria)

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.