Abstract
The topological invariants of monopoles are described for an arbitrary compact gauge groupG and Higgs fieldΦ in any representation. The results generalize those obtained recently for compact and simply connectedG andΦ in the adjoint representation. The cases when the residual symmetry group isH=U(1) orH=U(3) are worked out explicitly. This latter is needed to accommodate fractional electric charge with monopoles having one Dirac unit magnetic charge. The general theory is illustrated on the SU(5) monopole.
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