99-246 Giovanni Landi

Projective Modules of Finite Type and Monopoles over $S^2$ (45K, latex) Jun 29, 99

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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 )