English

Finite type knot invariants and calculus of functors

Algebraic Topology 2007-05-23 v2 Geometric Topology

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.

Keywords

Cite

@article{arxiv.math/0401440,
  title  = {Finite type knot invariants and calculus of functors},
  author = {Ismar Volic},
  journal= {arXiv preprint arXiv:math/0401440},
  year   = {2007}
}

Comments

Revised; to appear in Compositio Mathematica

R2 v1 2026-07-22T17:02:03.285Z