The realization of the decompositions of the 3-orbifold groups along the spherical 2-orbifold groups
It is a classical theorem of J. H. C. Whitehead that, subject to some minor conditions, if a fundamental group of a 3-manifold is a free product, then the 3-manifold is a connected sum -- that a decomposition as a free product at the group level can be realized by a decomposition at the manifold level. The authors extend this result as far as possible from 3-manifolds to 3-orbifolds. Their basic group-theoretic condition is that the fundamental 3-orbifold group should be a nontrivial free product with amalgamation over an orientable and spherical 2-orbifold group. The authors then prove that, except for very rare exceptions, there exists a spherical 2-suborbifold which realizes the decomposition geometrically. By example, they show that one of their rare exceptions actually occurs and that, in that case, the given group-theoretic decomposition cannot be realized geometrically.
scientific article; zbMATH DE number 1879086
scientific article