Gr1(R^(10,2))

The cohomology of $\text{Gr}_1(\mathbb{R}^{10,2})$

Poincaré polynomial: $$x^{9} y^{2} + x^{8} y^{2} + x^{7} y^{2} + x^{6} y^{2} + x^{5} y^{2} + x^{4} y^{2} + x^{3} y^{2} + x^{2} y + x y + 1$$ Generator count grid: Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_1(\mathbb{R}^{10,2}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{3,2}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{5,2}\mathbb{M}_2\oplus\Sigma^{6,2}\mathbb{M}_2\oplus\Sigma^{7,2}\mathbb{M}_2\oplus\Sigma^{8,2}\mathbb{M}_2\oplus\Sigma^{9,2}\mathbb{M}_2.$$