Small Cover的L-S畴数

母雪薇, 刘登品

数学学报 ›› 2021, Vol. 64 ›› Issue (1) : 59-64.

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PDF(381 KB)
数学学报 ›› 2021, Vol. 64 ›› Issue (1) : 59-64. DOI: 10.12386/A2021sxxb0004
论文

Small Cover的L-S畴数

    母雪薇, 刘登品
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Lusternik–Schnirelmann Category of Small Cover

    Xue Wei MU, Deng Pin LIU
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文章历史 +

摘要

我们证明了如下结论:任意n维smallcover的Lusternik-Schnirelmann畴数等于n;任意2n维toric-流形的Lusternik-Schnirelmann畴数等于n.我们的结果依赖于如下两个事实,一个是不等式cup(M)≤ cat(M)≤ dim(M)/r,它导致我们去计算cup(M).另一个事实是环面拓扑流形上同调环的明确表示,该表示使得cup(M)的计算变得容易.最后,我们进一步推广了相关结论.

Abstract

We proved that the Lusternik-Schnirelmann category of any n-dimensional small cover is n and that the Lusternik-Schnirelmann category of any 2n-dimensional toric manifold is also n. Our result depends on the two well-known facts, one is the inequality cup(M) ≤ cat(M) ≤ dim(M)/r which leads us to compute cup(M). The other is explicit expression on the cohomology ring of small cover which makes the calculation of cup(M) easier. Furthermore, we generalized the relevant conclusions.

关键词

small cover / toric-流形 / Lusternik-Schnirelmann畴数

Key words

small cover / toric manifold / Lusternik-Schnirelmann category

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导出引用
母雪薇, 刘登品. Small Cover的L-S畴数. 数学学报, 2021, 64(1): 59-64 https://doi.org/10.12386/A2021sxxb0004
Xue Wei MU, Deng Pin LIU. Lusternik–Schnirelmann Category of Small Cover. Acta Mathematica Sinica, Chinese Series, 2021, 64(1): 59-64 https://doi.org/10.12386/A2021sxxb0004

参考文献

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基金

国家自然科学基金资助项目(11401118)
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