# Article

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Keywords:
oriented Grassmann manifold; characteristic rank; Stiefel-Whitney class
Summary:
We use known results on the characteristic rank of the canonical \$4\$–plane bundle over the oriented Grassmann manifold \$\widetilde{G}_{n,4}\$ to compute the generators of the \$\mathbb{Z}_2\$–cohomology groups \$H^j(\widetilde{G}_{n,4})\$ for \$n=8,9,10,11\$. Drawing from the similarities of these examples with the general description of the cohomology rings of \$\widetilde{G}_{n,3}\$ we conjecture some predictions.
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