A note on the \(\mathbb Z_2\)-cohomology algebra of oriented Grassmann manifolds (Q2374454)

The cohomology of oriented Grassmann manifolds is studied in the paper. The authors completely determine the cohomology ring \(H^* (\tilde{G}_{n, 2}; \mathbb{Z}_2)\) for \(n\geq 4\) and the additive structure of \(H^* (\tilde{G}_{n, 3}; \mathbb{Z}_2)\) for \(n=6, 7, 8, 9,10, 11\). They demonstrate high expertise working with primary and secondary cohomology operations and combining various techniques to detect generators in the cohomology and the characteristic classes. They also signify usefulness of the characteristic rank of a vector bundle and the cup-length in such calculations