  This paper is dedicated to studying various aspects of topological defects,
appearing in mean-field theory treatments of physical systems such as ultracold
atomic gases and gauge field theories. We start by investigating topological
charge ambiguity and addition of topological charges using the mathematical
formalism of covering spaces, which clarifies many aspects these phenomena.
Subsequently, we classify topological defect configurations consisting of
several monopoles and unknotted ring defects in terms of homotopy groups and
fundamental group actions on them, thus generalizing the previous
classifications of a single monopole and a single unknotted ring defect.
Finally, we examine the decay of multiply charged topological monopoles under
small perturbations of the physical system, and analyze the conditions under
which multiply charged monopoles are inclined to split into several singly
charged monopoles.
