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This paper gives a partial description of the homotopy type of K, the space of long knots in R3. The primary result is the construction of a homotopy equivalence K ≃ C2(P ⊔ {∗}) where C2(P ⊔ {∗}) is(More)
We study Emb(Sj,Sn) the space of C∞ -smooth embeddings of spheres in spheres, Kn,j the space of ‘long’ embeddings of Rj in Rn , and spaces of embeddings of spheres in euclidean space Emb(Sj, Rn), and(More)
Abstract The operad of framed little discs is shown to be a cyclic operad. This answers a conjecture of Salvatore in the affirmative, posed at the workshop ‘Knots and Operads in Roma,’ at Università(More)