Kricker defined an invariant of knots in homology –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.
"Splitting formulas for the rational lift of the Kontsevich integral." Algebr. Geom. Topol. 20 (1) 303 - 342, 2020. https://doi.org/10.2140/agt.2020.20.303