2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156731We give a proof of the LMO conjecture which say that for any simply connectd simple Lie group $G$, the LMO invariant of rational homology 3-spheres recovers the perturvative invariant $τ^{PG}$. By Habiro-Le theorem, this implies that the LMO invariant is the universal quantum invariant of integral homology 3-spheres.11 pages, 5 figuresGeometric TopologyQuantum Algebra57M27text