Embedding calculus, Goodwillie calculus, and link invariants

In this talk, we will discuss how embedding calculus and Goodwillie’s functor calculus can be used together to study spaces of embeddings, and specifically examine the nature of their interaction.More precisely, the relationship between these two calculi is given by a lax morphism of towers that associates with each fake embedding the n-th Goodwillie approximation of the complement of its image.As an application, we show that Milnor invariants factor through the embedding tower for string links.