I will present a systematic study of the topology of Mikhailov's quarter and eighth-BPS giant gravitons in AdS_5 x S^5. These D3-branes are rigidly rotating 3-manifolds embedded into the 5-sphere compact space, which are dual to long, gauge-invariant, quarter and eighth-BPS operators in N=4 SYM theory by the AdS/CFT correspondence. How the topology is encoded in these operators remains an open question.