  Superfluid phenomena can be explained in terms of the topologies of the order
parameter and of the confining vessel. For example, currents in a toroidal
vessel can be characterized by a discrete and conserved quantity, the winding
number. In trapped Bose-Einstein condensates, the topology of the trap can be
characterized by the topology of the Thomas-Fermi surface of its N-particle
ground state. This can be altered during an experiment, so that a toroidal trap
may deform into a more spherical shape, allowing an initially persistent
current to decay into singly-quantized vortices. We investigate such a
procedure numerically, and confirm that the Thomas-Fermi prescription for the
trap topology gives an accurate picture of vortex formation.
