Rotational symmetry of ancient solutions to the Ricci flow in higher dimensions

We extend the second part of {Bre20} on the uniqueness of ancient κ-solutions to higher dimensions. In dimensions n ≥ 4, an ancient κ-solution is a nonflat, complete, ancient solution of the Ricci flow that is uniformly PIC and weakly PIC2; has bounded curvature; and is κ-noncollapsed. We show that the only noncompact ancient κ-solutions up to isometry are a family of shrinking cylinders, a quotient thereof, or the Bryant soliton.