Editing Geometrization conjecture (section)

===Hyperbolic geometry H<sup>3</sup>===
{{Main|Hyperbolic geometry}}
The point stabilizer is O(3, '''R'''), and the group ''G'' is the 6-dimensional Lie group O<sup>+</sup>(1, 3, '''R'''), with 2 components. There are enormous numbers of examples of these, and their classification is not completely understood. The example with smallest volume is the [[Weeks manifold]]. Other examples are given by the [[Seifert–Weber space]], or "sufficiently complicated" [[Dehn surgery|Dehn surgeries]] on [[link (knot theory)|link]]s, or most [[Haken manifold]]s. The geometrization conjecture implies that a closed 3-manifold is hyperbolic if and only if it is irreducible, [[atoroidal]], and has infinite fundamental group. This geometry can be modeled as a left invariant metric on the [[Bianchi classification|Bianchi group of type V or VII<sub>h≠0</sub>]]. Under Ricci flow, manifolds with hyperbolic  geometry expand.