99-246 Giovanni Landi
Projective Modules of Finite Type and Monopoles over \$S^2\$ (45K, latex) Jun 29, 99
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Abstract. 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.

Files: 99-246.src( 99-246.keywords , bundles.tex )