Embedding Calculus, Goodwillie Calculus and Link Invariants

Abstract: We study Goodwillie-Weiss embedding calculus through its relationship with Goodwillie's functor calculus. Specifically, building on a result of Tillmann and Weiss, we construct a functorial complement for (T_{n})-embeddings that takes values in Heuts's categorical (n)-excisive approximation of pointed spaces. We also establish an analogue of Stallings' theorem for lower central series in the context of (T_{n})-embeddings of (P \times I) into (D^{d}) for any compact manifold (P). As an application, we show that the embedding tower of string links detects Milnor invariants.