GENERALIZED HOPFIAN GROUPS IN HIGHER-DIMENSION SPACES
Abstract
We discuss the possibility of constructing topological solitons which generalize the Hopfian field configurations in the scalar Faddeev–Skyrme model extended to the case of spaces with the dimensions d = 4n – 1, nєZ. The fields of the model are the Hopf maps φ : R4n–1 → S2n with the usual vacuum boundary condition φ(x) → φ0 as x →∞. These soliton configurations are labelled by the topological invariant Q, which generalizes the first Hopf invariant of the map S3 → S2. We have demonstrated that there is a topological energy bound E ≥ c|Q|d⁄d+1, which generalizes the Vaculenko–Kapitansky inequality.
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