Misako Yokoyama

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

Abstract 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).

Computing the Topological Degree with Noisy Information

This paper addresses the problem of computing the topological degree of Lipschitz functions using noisy evaluations of function values as information. The uniformly bounded noise is considered. We prove that Kearfotts algorithm derives the exact topological degree using noisy information.

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

Abstract We 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 S 3 are composite.