Cartan方法及其在轴上同调中的应用

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2023-06-01 DOI:10.1016/j.exmath.2023.02.001

Yuan Liu

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引用次数: 0

摘要

本文旨在利用Cartan的原始方法证明闭立方体上的定理A和B，如果（i）次超过其实维数，或者（ii）sheaf是（局部）常数并且次为正，则提供闭立方体上sheaf上同调消失的不同证明。在第一种情况下，我们可以进一步使用Godement的论点来证明准紧拓扑流形的拓扑维数小于或等于其实维数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Cartan’s method and its applications in sheaf cohomology

This paper aims to use Cartan’s original method in proving Theorems A and B on closed cubes to provide a different proof of the vanishing of sheaf cohomology over a closed cube if either (i) the degree exceeds its real dimension or (ii) the sheaf is (locally) constant and the degree is positive. In the first case, we can further use Godement’s argument to show the topological dimension of a paracompact topological manifold is less than or equal to its real dimension.

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来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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