Geodesic
Bounds for the characteristic rank and cup-length of oriented Grassmann manifolds
Archivum mathematicum, Tome 54 (2018) no. 5, pp. 313-329 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We estimate the characteristic rank of the canonical $k$–plane bundle over the oriented Grassmann manifold $\widetilde{G}_{n,k}$. We then use it to compute uniform upper bounds for the $\mathbb{Z}_2$–cup-length of $\widetilde{G}_{n,k}$ for $n$ belonging to certain intervals.
We estimate the characteristic rank of the canonical $k$–plane bundle over the oriented Grassmann manifold $\widetilde{G}_{n,k}$. We then use it to compute uniform upper bounds for the $\mathbb{Z}_2$–cup-length of $\widetilde{G}_{n,k}$ for $n$ belonging to certain intervals.
DOI : 10.5817/AM2018-5-313
Classification : 55R25, 57R20, 57T15
Keywords: cup-length; Grassmann manifold; characteristic rank; Stiefel-Whitney class 
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     author = {Rusin, Tom\'a\v{s}},
     title = {Bounds for the characteristic rank and cup-length of oriented {Grassmann} manifolds},
     journal = {Archivum mathematicum},
     pages = {313--329},
     year = {2018},
     volume = {54},
     number = {5},
     doi = {10.5817/AM2018-5-313},
     mrnumber = {3887357},
     zbl = {06997358},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2018-5-313/}
}
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Rusin, Tomáš. Bounds for the characteristic rank and cup-length of oriented Grassmann manifolds. Archivum mathematicum, Tome 54 (2018) no. 5, pp. 313-329. doi: 10.5817/AM2018-5-313

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