The realization of the decompositions of the 3-orbifold groups along the spherical 2-orbifold groups

AbstractWe find spherical 2-orbifolds realizing the decompositions of the 3-orbifold fundamental groups, of which the amalgamated subgroups are isomorphic to the fundamental groups of orientable spherical 2-orbifolds. If one hypothesis fails, then there is a decomposition of the fundamental group of a 3-orbifold which cannot be realized. As an application of a weaker result of the Main Theorem we obtain a necessary and sufficient condition that unsplittable links embedded in S3 are composite