Research question
What topological sectors and observable charges are allowed by a specified gauge construction?
SMM/DTT direction
The gauge programme connects local comparisons with loop and global consistency conditions. Whether a model permits a monopole is a question about its mathematical configuration space and dynamics, not a consequence of a pictorial analogy.
What the construction must establish
Define the field or link variables, topology, charge observable, and energy conditions. State what follows within the model before comparing with particle or cosmological possibilities.