Abstract
We investigate the topological defects in atomic spin-1 and spin-2Bose–Einstein condensates by applying the homotopy group theory. With thisrigorous approach we clarify the previously controversial identification ofsymmetry groups and order parameter spaces for the spin-1 case, and showthat the spin-2 case provides a rare example of a physical system withnon-Abelian line defects, and the possibility to have winding numbers of1/3 and its multiples.
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