The topology and geometry of the moduli space, M2 , of degree 2 static solutions of the C P 1 model on a torus (spacetime T 2 R) are studied. It is proved that M2 is homeomorphic to the left coset space G=G0 where G is a certain eight-dimensional noncompact Lie group and G0 is a discrete subgroup of order 4. Low energy two-lump dynamics is approximated by geodesic motion on M2 with respect to a metric g deened by the restriction to M2 of the kinetic energy functional of the model. This lump dynamics decouples into a trivial \centre of mass" motion and nontrivial relative motion on a reduced moduli space. It is proved that (M2; g) is geodesically incomplete and has only nite diameter. A low dimensional geodesic submanifold is identiied and a full description of its geodesics obtained.