  In the homotopical study of spaces of smooth embeddings, the functor calculus
method (Goodwillie-Klein-Weiss manifold calculus) has opened up important
connections to operad theory. Using this and a few simplifying observations, we
arrive at an operadic description of the obstructions to deforming smooth
immersions into smooth embeddings. We give an application which in some
respects improves on recent results of Arone-Turchin and Dwyer-Hess concerning
high-dimensional variants of spaces of long knots.
