No compact split limit Ricci flow of type II from the blow-down

By Perelman's L-geodesic theory, we study the blow-down solutions on a noncompact -noncollapsed steady gradient Ricci soliton (Mⁿ, g) (n 4) with nonnegative curvature operator and positive Ricci curvature away from a compact set of M. We prove that any (n-1) -dimensional compact split ancient solution from the blow-down of (M, g) is of type I. The result is a generalization of our previous work from n=4 to any dimension.