# Embedding Calculus

Specialeforsvar: João Tiago Lobo Pires de Morais Fernandes

Titel: Embedding Calculus - A study of convergence and finiteness properties of the Goodwillie tower

Abstract: We study different aspects of the seminal work by Goodwillie, Klein, and Weiss on the homotopy type of embedding spaces [GK08][GK15][Goo90][Wei99][GW99]. These authors developed the machinery of embedding calculus, which associates to every pair M ⊂ N of smooth manifolds a tower of spaces approximating the homotopy type of Emb(M,N). Favorable properties of such towers have been used extensively in recent research in the study of the homotopy type of diffeomorphism groups of manifolds. We focus on the original proof of one of these properties: convergence. This proof takes advantage of a number of different tools in geometric topology and Homotopy Theory. We start by briefly introducing those tools and finish by applying this work to deduce finiteness properties of certain embedding spaces, following [Kup16] and [BKK21].

Vejleder: Søren Galatius
Censor: Martin Raussen, Ålborg Universitet