It is known from work of Perelman that any finite-time singularity of the Ricci flow on a compact three-manifold is modeled on an ancient $\kappa$-solution. We prove that the every noncompact ancient $\kappa$-solution in dimension $3$ is isometric to either the shrinking cylinders (or a quotient thereof), or the Bryant soliton.
Rotational symmetry of ancient solutions to the Ricci flow in dimension $3$ -- The compact case
On the Ricci Flow of Homogeneous Metrics on Spheres
On type-II singularities in Ricci flow on $\mathbb{R}^{N}$
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