Editing Geometrization conjecture (section)

===The geometry of the universal cover of SL(2, R)===
The [[universal cover]] of [[SL2(R)|SL(2, '''R''')]] is denoted <math>{\widetilde{\rm{SL}}}(2, \mathbf{R})</math>.  It fibers over '''H'''<sup>2</sup>, and the space is sometimes called "Twisted H<sup>2</sup> × R". The group ''G'' has 2 components. Its identity component has the structure <math>(\mathbf{R}\times\widetilde{\rm{SL}}_2 (\mathbf{R}))/\mathbf{Z}</math>.  The point stabilizer is O(2,'''R''').

Examples of these manifolds include: the manifold of unit vectors of the tangent bundle of a hyperbolic surface, and more generally the [[homology sphere|Brieskorn homology spheres]] (excepting the 3-sphere and the [[Poincaré dodecahedral space]]). This geometry can be modeled as a left invariant metric on the [[Bianchi classification|Bianchi group of type VIII or III]]. Finite volume manifolds with this geometry  are orientable and have the structure of a [[Seifert fiber space]]. The classification of such manifolds is given in the article on [[Seifert fiber space]]s. Under normalized Ricci flow manifolds with this geometry converge to a 2-dimensional manifold.