Abstract
This paper focuses on topological defects, appearing in mean-field-theory treatments of physical systems such as ultracold atomic gases and gauge field theories. We begin by investigating the 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.
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