Massive gauge bosons from the conservation of topological winding numbers

We consider a U(1) x SU(2) gauge theory on the four-dimensional manifold S^1 x S^3. If we make the assumption that only gauge transformations connected to the identity are allowed, the winding numbers of U(1) around S^1 and of SU(2) around S^3 become topological conserved quantities. We derive the effective theory for non-trivial winding numbers if all distances are small compared to the radii of the spheres. In the non-abelian case the gauge bosons become massive.