Embedding Calculus, Goodwillie Calculus and Link Invariants

2025/11/06 by Jin, Hyeonhee
#Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2511.04582

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 \(P × I\) into \(D^d\) for any compact manifold \(P\). As an application, we show that the embedding tower of string links detects Milnor invariants.

Citations

• Goodwillie approximations to higher categories
• Occupants in manifolds
• Higher Topos Theory

Related

• Delooping of high-dimensional spaces of string links
• Calculus of the embedding functor and spaces of knots
• Goodwillie Calculi
• Introduction to the manifold calculus of Goodwillie-Weiss
• Embedding calculus and grope cobordism of knots