Editing Ricci flow (section)

===Singularities in 4d Ricci flow===
In four dimensions very little is known about the possible singularities, other than that the possibilities are far more numerous than in three dimensions. To date the following singularity models are known
*<math>S^3 \times \mathbb{R} </math>
*<math>S^2 \times \mathbb{R}^2 </math>
*The 4d Bryant soliton
*Compact Einstein manifold of positive scalar curvature
*Compact gradient Kahler–Ricci shrinking soliton
*The FIK shrinker (discovered by [[M. Feldman]], [[Tom Ilmanen|T. Ilmanen]], [[D. Knopf]]) <ref>{{cite journal |first=D. |last=Maximo |s2cid=17651053 |title=On the blow-up of four-dimensional Ricci flow singularities |journal=J. Reine Angew. Math. |volume=2014 |issue=692 |year=2014 |pages=153–171 |doi=10.1515/crelle-2012-0080 |arxiv=1204.5967 }}</ref>
*The BCCD shrinker (discovered by [[Richard Bamler]], [[Charles Cifarelli]], [[Ronan Conlon]], and [[Alix Deruelle]])<ref>{{cite arXiv |last1=Bamler |first1=R. | last2=Cifarelli | first2=C. |last3=Conlon | first3=R. |last4=Deruelle |first4=A.|
date=2022 |title=A new complete two-dimensional shrinking gradient Kähler-Ricci soliton |eprint=2206.10785 |class=math.DG}}</ref> 
Note that the first three examples are generalizations of 3d singularity models. The FIK shrinker models the collapse of an embedded sphere with [[Intersection number|self-intersection number]]&nbsp;−1.