Finite type knot invariants and calculus of functors

Abstract

We associate a Taylor tower supplied by calculus of the embedding functor to the space of long knots and study its cohomology spectral sequence. The combinatorics of the spectral sequence along the line of total degree zero leads to chord diagrams with relations as in finite type knot theory. We show that the spectral sequence collapses along this line and that the Taylor tower represents a universal finite type knot invariant.

Revised; to appear in Compositio Mathematica

References in corpus (5)

• Embeddings from the point of view of immersion theory: Part I
• Integral Expressions for the Vassiliev Knot Invariants
• The Fundamental Theorem of Vassiliev Invariants
• The topology of spaces of knots
• New perspectives on self-linking

Cited by in corpus (8)

• Topology of spaces of knots in dimension 3
• Little cubes and long knots
• New perspectives on self-linking
• Operads and knot spaces
• Operadic actions on long knots and 2-string links
• Configuration space integrals and Taylor towers for spaces of knots
• On the homology of the space of knots
• A survey of Bott-Taubes integration