Finite type knot invariants and calculus of functors

Details Finite type knot invariants and calculus of functors Finite type knot invariants and calculus of functors

2004-01-30

arxiv.org/abs/math/0401440v2

Mathematics

Algebraic Topology

Revised; to appear in Compositio Mathematica

Scientific paper

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.

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