A dendroidal approach to Goodwillie-Weiss manifold calculus

by Dr Miguel Barata (Utrecht)

Tuesday Nov 4, 2025, 2:00 PM → 3:00 PM Europe/Paris

IMT 1R2 207 (Salle Pellos)

Manifold calculus is a technique developed by T. Goodwillie and M. Weiss for approximating the homotopy type of the space of smooth embeddings Emb(M,N) via the configuration spaces of the manifolds in question. Together with the convergence results by Goodwillie-Klein, embedding calculus has had a meaningful impact in both homotopy theory and differential topology, for instance for proving finiteness results for the homotopy groups of diffeomorphism groups.

In this talk I want to explain the Boavida-Weiss approach to manifold calculus in terms of operads and operadic right modules. I will describe how the study of these modules can be carried out using the language of trees and forests, via the formalism of dendroidal and forest spaces. Finally, I will explain how the Goodwillie-Weiss tower and its layers can be described using this language.