A universal equivariant finite type knot invariant defined from configuration space integrals

Abstract

In a previous article, we constructed an invariant Z for null-homologous knots in rational homology spheres, from equivariant intersections in configuration spaces. Here we present an equivalent definition of Z in terms of configuration space integrals, we prove that Z is multiplicative under connected sum, and we prove null Lagrangian-preserving surgery formulae for Z. Our formulae generalize similar formulae that are satisfied by the Kricker rational lift of the Kontsevich integral for null Borromean surgeries. They imply that Z is universal with respect to a natural filtration. According to results of Garoufalidis and Rozansky, they therefore imply that Z is equivalent to the Kricker lift of the Kontsevich integral for null-homologous knots with trivial Alexander polynomial in integral homology spheres.

76 pages

References in corpus (2)

• On the cube of the equivariant linking pairing for knots and 3-manifolds of rank one
• Splitting formulas for the LMO invariant of rational homology three-spheres

Cited by in corpus (4)

• An invariant of fiberwise Morse functions on surface bundle over $S^1$ by counting graphs
• Variation formulas for an extended Gompf invariant
• Finite type invariants of nullhomologous knots in 3-manifolds fibered over $S^1$ by counting graphs
• An introduction to finite type invariants of knots and 3-manifolds defined by counting graph configurations