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A dilute gas of Bose-Einstein condensed atoms in a non-rotated and axiallysymmetric harmonic trap is modelled by the time dependent Gross-Pitaevskiiequation. When the angular momentum carried by the condensate does not vanish,the minimum energy state describes vortices (or antivortices) that propagatearound the trap center. The number of (anti)vortices increases with the angularmomentum, and they repel each other to form Abrikosov lattices. Besidesvortices and antivortices there are also stagnation points where the superflowvanishes; to our knowledge the stagnation points have not been analyzedpreviously, in the context of the Gross-Pitaevskii equation. The Poincar\'eindex formula states that the difference in the number of vortices andstagnation points can never change. When the number of stagnation points issmall, they tend to aggregate into degenerate propagating structures. But whenthe number becomes sufficiently large, the stagnation points tend to pair upwith the vortex cores, to propagate around the trap center in regular latticearrangements. There is an analogy with the geometry of the Kosterlitz-Thoulesstransition, with the angular momentum of the condensate as the external controlparameter instead of the temperature.

Poincar\'e index formula and analogy with the Kosterlitz-Thouless transition in a non-rotated cold atom Bose-Einstein condensate