Cartan’s method and its applications in sheaf cohomology

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

引用次数: 0

Abstract

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.

查看原文本刊更多论文

Cartan方法及其在轴上同调中的应用

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。

求助全文

约1分钟内获得全文求助全文

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

期刊介绍： Our aim is to publish papers of interest to a wide mathematical audience. Our main interest is in expository articles that make high-level research results more widely accessible. In general, material submitted should be at least at the graduate level.Main articles must be written in such a way that a graduate-level research student interested in the topic of the paper can read them profitably. When the topic is quite specialized, or the main focus is a narrow research result, the paper is probably not appropriate for this journal. Most original research articles are not suitable for this journal, unless they have particularly broad appeal.Mathematical notes can be more focused than main articles. These should not simply be short research articles, but should address a mathematical question with reasonably broad appeal. Elementary solutions of elementary problems are typically not appropriate. Neither are overly technical papers, which should best be submitted to a specialized research journal.Clarity of exposition, accuracy of details and the relevance and interest of the subject matter will be the decisive factors in our acceptance of an article for publication. Submitted papers are subject to a quick overview before entering into a more detailed review process. All published papers have been refereed.