Topology of the embedding spaces via configuration space integrals, operads and the calculus of functors

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I continued the study of the spaces of embedding between spheres. I showed that the space fE called “the space of embeddings modulo immersions” is an iterated loop space of the topological Stiefel manifold. As applications I obtained;(1) A BV-algebra structure on the homology of fE(2) An alternative proof in terms of topological Stiefel manifolds of the fact that the “spinning” operation gives rise to an isomorphism of the lower dimensional homotopy groups of the embedding spaces.