The cohomology of $\text{Gr}_1(\mathbb{R}^{5,1})$
Poincaré polynomial: $$x^{4} y + x^{3} y + x^{2} y + x y + 1$$ Generator count grid:
1
1
1
1
1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_1(\mathbb{R}^{5,1}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{3,1}\mathbb{M}_2\oplus\Sigma^{4,1}\mathbb{M}_2.$$