Cobordism Independence of Grassmann Manifolds

[摘要] This note proves that, for $F=mathbb{R},mathbb{C}$ or $mathbb{H}$, the bordism classes of all non-bounding Grassmannian manifolds $G_k(F^{n+k})$, with 𝑘 < 𝑛 and having real dimension 𝑑, constitute a linearly independent set in the unoriented bordism group $mathfrak{N}_d$ regarded as a $mathbb{Z}_2$-vector space.

[学科分类] 数学（综合）

[关键词] Grassmannians;bordism;Stiefel-Whitney class.