|$\chi(\mathcal{B})\lt0$||$\chi(\mathcal{B})=0$||$\chi(\mathcal{B})\gt0$|
|$e(f)=0$||$\mathbb H^2\times\mathbb{R}$||$\mathbb{R}^3$||$\mathbb S^2\times \mathbb{R}$|
|$e(f)\not=0$||$\widetilde{SL_2}$|Nil|$\mathbb S^3$|
 |$\chi(\mathcal{B})\lt0$||$\chi(\mathcal{B})=0$||$\chi(\mathcal{B})\gt0$|
|$e(f)=0$||$\mathbb H^2\times\mathbb{R}$||$\mathbb{R}^3$||$\mathbb S^2\times \mathbb{R}$|
|$e(f)\not=0$||$\widetilde{SL_2}$|Nil|$\mathbb S^3$|
 |$\chi(\mathcal{B})\lt0$||$\chi(\mathcal{B})=0$||$\chi(\mathcal{B})\gt0$|
|$e(f)=0$||$\mathbb H^2\times\mathbb{R}$||$\mathbb{R}^3$||$\mathbb S^2\times \mathbb{R}$|
|$e(f)\not=0$||$\widetilde{SL_2}$|Nil|$\mathbb S^3$|
 |$\chi(\mathcal{B})\lt0$||$\chi(\mathcal{B})=0$||$\chi(\mathcal{B})\gt0$|
|$e(f)=0$||$\mathbb H^2\times\mathbb{R}$||$\mathbb{R}^3$||$\mathbb S^2\times \mathbb{R}$|
|$e(f)\not=0$||$\widetilde{SL_2}$|Nil|$\mathbb S^3$|
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