Thurston's Geometrization Conjecture
When a topological manifold of dimension $3$ has been split into its connected sum and the Jaco-Shalen-Johannson torus decomposition, the remaining components each admit exactly one of the following geometries:
- $(1): \quad$ Euclidean geometry
- $(2): \quad$ Hyperbolic geometry
- $(3): \quad$ Spherical geometry
- $(4): \quad$ The geometry of $\mathbb S^2 \times \R$
- $(5): \quad$ The geometry of $\mathbb H^2 \times \R$
- $(7): \quad$ Nil geometry
- $(8): \quad$ Sol geometry
- $\mathbb S^2$ is the 2-sphere
- $\mathbb H^2$ is the hyperbolic plane.
Source of Name
This entry was named for William Paul Thurston.
- Weisstein, Eric W. "Thurston's Geometrization Conjecture." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ThurstonsGeometrizationConjecture.html