Smooth 4-dimensional Poincaré conjecture

Dimension four is the one place where topological and smooth categories come apart most wildly: $\mathbb{R}^4$ alone carries uncountably many smooth structures. The topological version is Freedman's theorem. Whether an exotic smooth 4-sphere exists is open, and it is one of the central questions of low-dimensional topology.

What would settle it

Lean statement in formal-conjectures (Poincaré variants)

Sources

• Wikipedia: Generalized Poincaré conjecture

Geometry and topology · Mathematics