 Kaluza-Klein monopole

A gravitational magnetic monopole for a compact circle, whose fibre is nontrivially twisted over a surrounding two-sphere. With flat spectator directions its nonsingular local geometry is a Taub–NUT space. Reducing along the M-circle yields the D6-brane. The magnetic dual of the IIB circle vector is instead a five-brane in nine noncompact dimensions.

// Target: geometry-and-topology.bigb