 98743 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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