Abstract
We study geometrically the coadjoint orbits of the central extensions of gauge groups over arbitrary manifolds. We show that these orbits are classified by a dimension one foliation with a transverse measure, together with a leafwise connection. For the case of a two-dimensional torus with standard trivial foliation, we show that the holonomies along the leaves give a complete invariant for the regular coadjoint orbits. We investigate in detail the Kronecker foliation of a torus using a new construction which we call asymptotic holonomy.
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