Calculus of the embedding functor and spaces of knots

Mathematics – Algebraic Topology

Scientific paper

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A survey prepared for the AIM Workshop On Moduli Spaces of Knots

Scientific paper

We give an overview of how calculus of the embedding functor can be used for the study of long knots and summarize various results connecting the calculus approach to the rational homotopy type of spaces of long knots, collapse of the Vassiliev spectral sequence, Hochschild homology of the Poisson operad, finite type knot invariants, etc. Some open questions and conjectures of interest are given throughout.

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