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In [4], we proved that every noncompact ancient $\kappa$-solution to theRicci flow in dimension $3$ is either locally isometric to a family ofshrinking cylinders, or isometric to the Bryant soliton. In the same paper, weannounced that the same method implies that compact ancient $\kappa$-solutionsare rotationally symmetric. In this note we provide the details of thisargument.

Rotational symmetry of ancient solutions to the Ricci flow in dimension $3$ -- The compact case