The geometric realizations of the decompositions of 3-orbifold fundamental groups

We introduce a type of generalized orbifold called an “orbifold composition”. We study their topology and the extensions and deformations of the maps between them. As the main goal, we obtain the theorems which yield the geometric realizations of amalgamated free products and HNN extensions of 3-orbifold fundamental groups. They are extensions of results of Feustel (1972; 1973) and Feustel and Gregorac (1973).