2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106298We prove that the quantum SO(3)-invariant of an arbitrary 3-manifold $M$ is always an algebraic integer, if the order of the quantum parameter is co-prime with the order of the torsion part of $H_1(M,\BZ)$. An even stronger integrality, known as cyclotomic integrality, was established by Habiro for integral homology 3-spheres. Here we generalize Habiro's result to all rational homology 3-spheres.19 pages. Minor typos correctedGeometric TopologyQuantum Algebra57M25text