Spaces of smooth embeddings, disjunction and surgery

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Operads and knot spaces (2004, methodology): “tower (or for the homotopy ﬁbers of Tk →Tk−1, which are called layers), either as spaces of sections as in section nine of [43] or as mapping spaces with strongly deﬁned equivariance properties as in [16]. In the case of knots we have developed three closely-related models for these polynomial appro”
Finite type knot invariants and the calculus of functors (2004, background): “ to the stages of the Taylor tower for K. 4. Taylor towerfor thespaceof knots Building on general theory of calculus of functors developed by Goodwillie [13, 14, 15], Weiss develops in [32] (also see [17]) a certain tower for studying the space of embeddings of one manifold in another. The stages of”
New perspectives on self-linking (2003, background): “The computations of these homotopy types can be determined quickly if one cites Theorem 2.17 and builds on the analysis of the embedding tower for knots of Goodwillie and Weiss in section five of [16], or alternately if one uses the cosimplicial model for this embedding tower as first envisioned by ”