Finite type knot invariants and the calculus of functors

By Ismar Volic. Compositio Mathematica, 2004

47 citations recorded by the source corpus.

We associate a Taylor tower supplied by the 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b85420a9382860f3d0be1147d5629b510c38c806

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Dev Sinha
2. Victor Turchin
3. Victor Tourtchine
4. Ismar Volic
5. B. Munson
6. Ryan Budney

In Mathematical Physics

1. Dev Sinha
2. Victor Turchin
3. Victor Tourtchine
4. Ismar Volic
5. P. Lambrechts
6. B. Munson
7. Ryan Budney

Citations in the corpus

• The topology of spaces of knots: cosimplicial models (2002, methodology): “The analogy between our cosimplicial model for a knot space and the cosimplicial model for loop spaces is made precise in Section 5 of [43] and Section 5 of [ 54 ].”
• Operads and knot spaces (2004, result): “Building on work of Goodwillie, Klein and Weiss [44, 15, 19, 18], and Volic [ 41 , 42], we have the following.”