Vacuum-boundary degree as a defect charge
= Vacuum-boundary degree as a defect charge
{title2=$Q=\deg(S^{d-1}\to S^{d-1})$}
A normalized vacuum field on a sphere surrounding a core can define $S^{d-1}\to S^{d-1}$ with integer <topological degree>. Nonzero degree obstructs its extension through the enclosed ball while staying in the <vacuum manifold>. This accounts for the <winding number> of a <vortex> and the spherical degree of a <magnetic monopole>, with the appropriate vacuum targets.