98-743 Giovanni Landi

Deconstructing Monopoles and Instantons (56K, LATeX 2e) Dec 7, 98

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Abstract. We give a unifying description of the Dirac monopole on the $2$-sphere $S^2$, of a graded monopole on a $(2,2)$-supersphere $S^{2,2}$ and of the BPST instanton on the $4$-sphere $S^4$, by constructing a suitable global projector $p$ via equivariant maps. This projector determines the projective modules of finite type of sections of the corresponding vector bundle. The canonical connection $\nabla = p \circ d$ is used to compute the topological charge which is found to be equal to $-1$ for the three cases. The transposed projector $q=p^t$ gives the value $+1$ for the charges. We also study the invariance under the action of suitable Lie groups.

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