  A dilute gas of Bose-Einstein condensed atoms in a non-rotated and axially
symmetric harmonic trap is modelled by the time dependent Gross-Pitaevskii
equation. When the angular momentum carried by the condensate does not vanish,
the minimum energy state describes vortices (or antivortices) that propagate
around the trap center. The number of (anti)vortices increases with the angular
momentum, and they repel each other to form Abrikosov lattices. Besides
vortices and antivortices there are also stagnation points where the superflow
vanishes; to our knowledge the stagnation points have not been analyzed
previously, in the context of the Gross-Pitaevskii equation. The Poincar\'e
index formula states that the difference in the number of vortices and
stagnation points can never change. When the number of stagnation points is
small, they tend to aggregate into degenerate propagating structures. But when
the number becomes sufficiently large, the stagnation points tend to pair up
with the vortex cores, to propagate around the trap center in regular lattice
arrangements. There is an analogy with the geometry of the Kosterlitz-Thouless
transition, with the angular momentum of the condensate as the external control
parameter instead of the temperature.
