Embeddings from the point of view of immersion theory : Part II

Abstract

Let $M$ and $N$ be smooth manifolds. For an open $V\subset M$ let $emb\left(V,N\right)$ be the space of embeddings from $V$ to $N$. By the results of Goodwillie and Goodwillie–Klein, the cofunctor $V\mapsto emb\left(V,N\right)$ is analytic if $dim\left(N\right)-dim\left(M\right)\ge 3$. We deduce that its Taylor series converges to it. For details about the Taylor series, see Part I