  We consider the moduli space of flat G-bundles over the twodimensional torus,
where G is a real, compact, simple Lie group which is not simply connected. We
show that the connected components that describe topologically non-trivial
bundles are isomorphic as symplectic spaces to moduli spaces of topologically
trivial bundles with a different structure group. Some physical applications of
this isomorphism which allows to trade topological non-triviality for a change
of the gauge group are sketched.
