# Calculus of the embedding functor and spaces of knots

Research paper by Ismar Volic

Indexed on: 11 Jan '06Published on: 11 Jan '06Published in: Mathematics - Algebraic Topology

#### Abstract

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.