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Keywords:
cup-length; Grassmann manifold; characteristic rank; Stiefel-Whitney class
cup-length; Grassmann manifold; characteristic rank; Stiefel-Whitney class
Summary:
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.
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