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arXiv · 2305.09862

Cup-length of oriented Grassmann manifolds via Gr\"obner bases

Uroš A. Colović·Branislav I. Prvulović
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Abstract

The aim of this paper is to prove a conjecture made by T. Fukaya in 2008. This conjecture concerns the exact value of the $\mathbb Z_2$-cup-length of the Grassmann manifold $\widetilde G_{n,3}$ of oriented $3$-planes in $\mathbb R^n$. Along the way, we calculate the heights of the Stiefel--Whitney classes of the canonical vector bundle over $\widetilde G_{n,3}$.

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Uroš A. Colović, Branislav I. Prvulović. 2023-05-17. Cup-length of oriented Grassmann manifolds via Gr\"obner bases. https://arxiv.org/abs/2305.09862

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