The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant

TL;DR

This paper proves that the LMO invariant is a universal invariant from which all perturbative invariants of rational homology 3-spheres can be derived, confirming a longstanding conjecture and linking it to quantum invariants.

Contribution

It demonstrates the universality of the LMO invariant for perturbative invariants of rational homology 3-spheres, confirming a key conjecture in the field.

Findings

LMO invariant is universal among perturbative invariants

Perturbative invariants can be recovered from the LMO invariant

Implication that the LMO invariant dominates quantum invariants of integral homology 3-spheres

Abstract

We show that the perturbative ${\frak g}$ invariant of rational homology 3-spheres can be recovered from the LMO invariant for any simple Lie algebra ${\frak g}$, i.e, the LMO invariant is universal among the perturbative invariants. This universality was conjectured in [25]. Since the perturbative invariants dominate the quantum invariants of integral homology 3-spheres [13,14,15], this implies that the LMO invariant dominates the quantum invariants of integral homology 3-spheres.