Splitting formulas for the rational lift of the Kontsevich integral

Abstract

Kricker defined an invariant of knots in homology 3-spheres which is a rational lift of the Kontsevich integral, and proved with Garoufalidis that this invariant satisfies splitting formulas with respect to a surgery move called null-move. We define a functorial extension of the Kricker invariant and prove splitting formulas for this functorial invariant with respect to null Lagrangian-preserving surgery, a generalization of the null-move. We apply these splitting formulas to the Kricker invariant.

Minor corrections. References updated. To appear in Algebraic & Geometric Topology

References in corpus (4)

• Splitting formulas for the LMO invariant of rational homology three-spheres
• On Kirby calculus for null-homotopic framed links in 3-manifolds
• Finite type invariants of knots in homology 3-spheres with respect to null LP-surgeries
• Equivariant triple intersections