On \(\kappa \)-solutions and canonical neighborhoods in 4d Ricci flow (Q6547191)

Motivated by the now advanced understanding of the Ricci flow in dimension three, this note discusses the \(4\)-dimensional Ricci flow and a conjectural picture for the structure of its singularities. The author conjectures a list of singularity models (ancient \(\kappa\)-solutions) and demonstrates the existence of a new one-parameter family of \(\mathbb{Z}_2^2 \times O_3\)-symmetric ancient oval solutions in dimension four. Finally, the author discusses the plausibility of existence and uniqueness for a \(4\)-dimensional Ricci flow through singularities. The author conjectures that uniqueness holds through cylindrical singularities, but nonuniqueness may occur in the presence of quotient necks.