 99246 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.
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