  We study analytically and numerically the core structure of global vortices
forming on topologically deformed brane-worlds with a single toroidally compact
extra dimension. It is shown that for an extra dimension size larger than the
scale of symmetry breaking the magnitude of the complex scalar field at the
vortex center can dynamically remain non-zero. Singlevaluedness and regularity
are not violated. Instead, the winding escapes to the extra dimension at the
vortex center. As the extra dimension size decreases the field magnitude at the
core dynamically decreases also and in the limit of zero extra dimension size
we reobtain the familiar global vortex solution. Extensions to other types of
defects and gauged symmetries are also discussed.
