Geodesic
Bounds for the characteristic rank and cup-length of oriented Grassmann manifolds
Archivum mathematicum, Tome 54 (2018) no. 5, pp. 313-329.

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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.
DOI : 10.5817/AM2018-5-313
Classification : 55R25, 57R20, 57T15
Keywords: cup-length; Grassmann manifold; characteristic rank; Stiefel-Whitney class 
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     title = {Bounds for the characteristic rank and cup-length of oriented {Grassmann} manifolds},
     journal = {Archivum mathematicum},
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     publisher = {mathdoc},
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     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. http://geodesic.mathdoc.fr/articles/10.5817/AM2018-5-313/

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