Slow equivariant lump dynamics on the two sphere

The low-energy, rotationally equivariant dynamics of n lumps on S² is studied within the approximation of geodesic motion in the moduli space of static solutions . The volume and curvature properties of are computed. By lifting the geodesic flow to the completion of an n-fold cover of , a good understanding of nearly singular lump dynamics within this approximation is obtained. The limit of large domain radius is examined and a prediction for the rate of collapse of coincident lumps in the plane extracted.