Projective modules of finite type and monopoles over \(S^2\) (Q5927605)

An useful idea in noncommutative geometry is the following: the substitution of vector bundles by projective modules of finite type. The paper presents this correspondence for vector bundles over the two-dimensional sphere. This is given by a global projector; which determines the module of sections of the vector bundles on which monopoles live, as the image from a suitable module. The canonical connection is used to compute the topological charge. In fact, transposed projectors give opposite values for the charges. Also, the construction of a partial isometry yielding the equivalence between the tangent projector and the real form of the charge 2 projector is explained.