Embedding Calculus, Goodwillie Calculus and Link Invariants

Embedding calculus provides a systematic method for approximating spaces of embeddings from configuration spaces. In this talk, we study how taking complements of embeddings can be done in this setting. It turns out that Goodwillie calculus provides the natural setting for complements in embedding calculus. As an application, we show that the Milnor invariants of string links factor through the embedding tower for string links.