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The quantum cohomology of CP^1 is generated by some potential (Frobeniusmanifold) that also has an interpretation as a potential of some harmonic map.Actually, the potential induces harmonic maps into three different symmetricspaces and each of these harmonic maps induces an immersion of an integrablesurface. The final goal of this paper is to investigate if any of theassociated immersions closes around the singularity at z=0 (none does). Thecrucial tool for deciding this question is the main technical result of thepaper, which states that the dressing isotropy of the CP^1 potential istrivial.

Triviality of the dressing isotropy for a Smyth-type potential and nonclosing of the resulting CMC surfaces