Title: Operads and embedding spaces
Speaker: Ryan Budney
Speaker Info: University of Victoria
Brief Description:
Special Note:
Abstract:
A pair of classical operations on knots known as connect-sums and satellite operations fit into the action of an operad on the space of knots. In dimension 3 this operad has the homotopy-type of a finite-dimensional suboperad, the proof of which uses many of the key structure theorems of 3-manifold theory. I'll outline this set-up and describe current work on what this operad has to say about knot theory. Things I'm currently working on include: bar constructions, what is known or conjectured about how the bar constructions fit with embedding calculus and Vassiliev invariants, as well as how these operads might fit into the description of high-dimensional embedding spaces and some inevitable relations with algebraic k-theory.Date: Monday, January 14, 2013