Geodesic
A note on the cohomology ring of the oriented Grassmann manifolds $\widetilde{G}_{n,4}$
Archivum mathematicum, Tome 55 (2019) no. 5, pp. 319-331 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2019-5-319
Classification : 55R25, 57R20, 57T15
Keywords: oriented Grassmann manifold; characteristic rank; Stiefel-Whitney class 
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Rusin, Tomáš. A note on the cohomology ring of the oriented Grassmann manifolds $\widetilde{G}_{n,4}$. Archivum mathematicum, Tome 55 (2019) no. 5, pp. 319-331. doi: 10.5817/AM2019-5-319

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