The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant (Q2892849)

For \(\mathfrak{g}\) a simple Lie algebra, applying the weight system \(\hat{W}_{\mathfrak{g}}\) to the LMO invariant \(\hat{Z}^{LMO}(M)\) of a rational homology 3-sphere \(M\), the authors obtain a multiple of the perturbative \(\mathfrak{g}\) invariant \(\tau^{\mathfrak{g}}(M)\) of \(M\), from which the conclusion follows: the LMO invariant is universal among the perturbative invariants (which answers a conjecture from [\textit{T. T. Q. Le} and \textit{J. Murakami}, Compos. Math. 102, No.1, 41--64 (1996; Zbl 0851.57007)]), hence it dominates the quantum invariants of integral homology 3-spheres. The paucity of connections between the multiple proofs being provided leaves the reader wanting for more. The ``geometric'' proof of Proposition 3.5 is inherently analytical. The reader is invited to read the papers from which what is now known as the LMO invariant came to be. One should start with \textit{Thang T. Q. Le} and \textit{J. Murakami} [Commun. Math. Phys. 168, No. 3, 535--562 (1995; Zbl 0839.57008)], followed by \textit{Thang T. Q. Le}, et al., [J. Pure Appl. Algebra 121, No. 3, 271-291 (1997; Zbl 0882.57005)].