A Haefliger style description of the embedding calculus tower
Let M and N be smooth manifolds. The calculus of embeddings produces, for every k ?1, a best degree 6k polynomial approximation to the cofunctor taking an open V ! M to the space of embeddings from V to N. In this paper, a description of these polynomial approximations in terms of equivariant mapping spaces is given, for k ?2. The description is new only for k ?3. In the case k =2 we recover Hae! iger’s approximation and the known result that it is the best degree 62 approximation. ? 2002 Published by Elsevier Science Ltd. MSC: Primary 57R40; 57R52; Secondary 57S17; 58A03