Proposition 2.3 . [03GG]

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Proposition 2.3.

For $\Nil^{3}_{b}$ , we have $b_{1}(\Nil^{3}_{b})=b_{2}(\Nil^{3}_{b})=2$ , and the de Rham cohomology group $H^{1}(\Nil^{3}_{b})$ is generated by $\pi^{*}dx$ and $\pi^{*}dy$ .