面向格拉斯曼流形 G͠ 2 t,3 的模 2 同调中的格氏基

Pub Date : 2024-05-28 DOI:10.1515/ms-2024-0015

Uroš A. Colović, Branislav I. Prvulović

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引用次数: 0

摘要

对于 n 的 2 次幂，我们给出了对ℝ n 中定向 3 平面的格拉斯曼流形 G͠ n,3 的同调代数 H *(G͠ n,3; ℤ2)的完整描述。为此，我们要为与这个同调代数密切相关的理想找到一个还原的格氏基。利用这个格氏基，我们还提出了 H *(G͠ n,3; ℤ2)的加法基。

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Gröbner bases in the mod 2 cohomology of oriented Grassmann manifolds G͠ 2 t,3

For n a power of two, we give a complete description of the cohomology algebra H *(G͠ n,3; ℤ2) of the Grassmann manifold G͠ n,3 of oriented 3-planes in ℝ n . We do this by finding a reduced Gröbner basis for an ideal closely related to this cohomology algebra. Using this Gröbner basis we also present an additive basis for H *(G͠ n,3; ℤ2).

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