| Field | Geometric topology |
|---|---|
| Conjectured by | William Thurston |
| Conjectured in | 1980 |
| First proof by | Grigori Perelman |
| First proof in | 2006 |
| Implied by | Geometrization conjecture |
| Equivalent to | Poincaré conjecture Spherical space form conjecture |
William Thurston's elliptization conjecture states that a closed 3-manifold with finite fundamental group is spherical, i.e. has a Riemannian metric of constant positive sectional curvature.