  Generalized Bose operators correspond to reducible representations of the
harmonic oscillator algebra. We demonstrate their relevance in the construction
of topologically non-trivial solutions in noncommutative gauge theories,
focusing our attention to flux tubes, vortices, and instantons. Our method
provides a simple new relation between the topological charge and the number of
times the basic irreducible representation occurs in the reducible
representation underlying the generalized Bose operator. When used in
conjunction with the noncommutative ADHM construction, we find that these new
instantons are in general not unitarily equivalent to the ones currently known
in literature.
