This paper presents a numerical study of the flow topologies of three-dimensional (3D) flows in a high pressure compressor stator blade row without and with boundary layer aspiration on the hub wall. The stator blade is representative of the first stage operating under transonic inlet conditions and the blade design encourages development of highly complex 3D flows. The blade has a small tip clearance. The computational fluid dynamics (CFD) studies show progressive increase of hub corner stall with the increase in incidence. Aspiration is implemented on the hub wall via a slot in the corner between the hub wall and the suction surface. The CFD studies show aspiration to be sensitive to the suction flow rate; lower rate leads to very complex flow structures and increased level of losses whereas higher rate renders aspiration effective for control of hub corner separation. The flow topologies are studied by trace of skin friction lines on the walls. The nature of flow can be explained by the topological rules of closed separation. Furthermore, a deeper analysis is done for a particular case with advanced criterion to test the non-degeneracy of critical points in the flow field. This paper presents a numerical study of the flow topologies of three-dimensional (3D) flows in high pressure compressor stator blade row without and with boundary layer aspiration on the hub wall. The stator blade is representative of the first stage operating under transonic inlet conditions and the blade design encourages development of highly complex 3D flows. The blade has a small tip clearance. The computational fluid dynamics (CFD) studies show progressive increase of hub corner stall with the increase in incidence. Aspiration is implemented on the hub wall via a slot in the corner between the hub wall and the suction surface. The CFD studies show aspiration to be sensitive to the suction flow rate; lower rate leads to very complex flow structures and increased level of losses and higher rate renders aspiration effective for control of hub flow separation. The flow topologies are studied by trace of skin friction lines on the walls. The nature of flow can be explained by the topological rules of closed separation. Furthermore, a deeper analysis is done for a particular case with advanced criterion to test the non-degeneracy of critical points in the flow field.