Unique Asymptotics of Compact Ancient Solutions toThree-DimensionalRicci Flow

We consider compact ancient solutions to the three-dimensional Ricci flow that are kappa-noncollapsed. We prove that such a solution either is a family of shrinking round spheres or has a unique asymptotic behavior ast -> - infinity, which we describe. This analysis applies in particular to the ancient solution constructed by Perelman. (c) 2020 Wiley Periodicals LLC