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
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Key words
small cover /
toric manifold /
Lusternik-Schnirelmann category
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参考文献
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脚注
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基金
国家自然科学基金资助项目(11401118)
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