Meromorphic functions and the topology of giant gravitons

Using Mikhailovʼs map from holomorphic functions to supersymmetric D3-brane solutions, we show how to construct giant gravitons in AdS5×S5 with toroidal topologies. In the 1/4-BPS sector we show that these are always of the form ♯K(S2×S1), and in the limit in which this becomes a set of m+n perpendicular spherical giants re-connected near to their intersections, we find K in terms of m, n. In the 1/8-BPS sector we find a similar class of solutions