Physics – Mathematical Physics
Scientific paper
1999-05-19
J.Geom.Phys. 37 (2001) 47-62
Physics
Mathematical Physics
15 pages, Latex
Scientific paper
We give a unifying description of all inequivalent vector bundles over the 2-dimensional sphere $S^2$ by constructing suitable global projectors $p$ via equivariant maps. Each projector determines the projective module of finite type of sections of the corresponding complex rank 1 vector bundle over $S^2$. The canonical connection $\nabla = p \circ d$ is used to compute the topological charges. Transposed projectors gives opposite values for the charges, thus showing that transposition of projectors, although an isomorphism in K-theory, is not the identity map. Also, we construct the partial isometry yielding the equivalence between the tangent projector (which is trivial in K-theory) and the real form of the charge 2 projector.
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