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A noncommutative uniton theory. (English) Zbl 1187.58021
Summary: Harmonic two-spheres in the unitary group may be constructed and described in terms of unitons. We present an analogue of this theory for those solutions of the noncommutative $$U(1)$$ sigma-model that may be represented as finite-dimensional perturbations of zero-energy solutions. In particular, we establish that the energy of every such solution is an integer multiple of $$8\pi$$, describe all solutions of small energy and give many explicit examples of non-Grassmannian solutions.
##### MSC:
 58E20 Harmonic maps, etc. 53C35 Differential geometry of symmetric spaces