Topological content of dimensional reduction

We consider supersymmetric Yang-Mills theories which have nontrivial topological features and show that in this case the dimensional-reduction technique has a topological content. We find that a central charge of topological origin can be obtained, by dimensional reduction, from a topological charge in a higher-dimensional supersymmetry algebra (but not from an extra component of P/sub μ/). We interpret this fact in terms of commutative diagrams of spheres