On the mod 2 cohomology algebra of oriented Grassmannians (Q6612004)

Grassmannians are classical objects of interest in mathematics. However, very little is known about the cohomology ring (even with \(\mathbb{Z}_2\) coefficients) of oriented Grassmannians except for \(\widetilde{G}_{n,1}\) and \(\widetilde{G}_{n,2}\). Building on works (and related computations) by several predecessors, in this manuscript the authors give a complete description (Theorem 1.1) of the cohomology ring \(H^*(\widetilde{G}_{n,3};\mathbb{Z}_2)\) when \(n\in\{2t-1,2t-2, 2t-3\}\) and \(t\geq 3\).