Thurston geometry
= Thurston geometry
{c}
The eight simply connected three-dimensional homogeneous model geometries are $S^3$, $\mathbb R^3$, $\mathbb H^3$, $S^2\times\mathbb R$, $\mathbb H^2\times\mathbb R$, $\widetilde{\operatorname{SL}}_2(\mathbb R)$, $\mathrm{Nil}$ and $\mathrm{Sol}$. A geometric structure is a locally homogeneous structure obtained as a quotient of a model by a discrete freely acting isometry group, equivalently with compatible model charts.