# Splitting formulas for the rational lift of the Kontsevich integral

## TL;DR

This paper extends the Kricker invariant of knots in homology 3-spheres to a functorial setting and proves splitting formulas for it under null Lagrangian-preserving surgeries, generalizing previous results.

## Contribution

It introduces a functorial extension of the Kricker invariant and establishes splitting formulas for this extension under a broader class of surgeries.

## Key findings

- Proves splitting formulas for the extended invariant.
- Generalizes null-move splitting formulas to null Lagrangian-preserving surgeries.
- Enhances understanding of knot invariants in homology 3-spheres.

## 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.