The paper shows how vector topological charges for topological excitations in nonlinear #sigma#-models on compact one-dimensional spaces T_G and G/T_G can be defined (here G is a simple compact Lie group and T_G is its maximal commutative subgroup). Explicit solutions, their energies and interactions between different topological charges have been obtained. A possibility of topological interpretation of quantum numbers of groups and particles is discussed.
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