Cartan's method and its applications in sheaf cohomology

被引：0
|
作者：
Liu, Yuan [1 ]
机构：
[1] Univ Sci & Technol China, Inst Geometry & Phys, Hefei 230026, Anhui, Peoples R China
来源：
EXPOSITIONES MATHEMATICAE | 2023年 / 41卷 / 02期
关键词：
Sheaf cohomology; Cartan's method; Topological dimension;
D O I：
10.1016/j.exmath.2023.02.001
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.& COPY; 2023 Elsevier GmbH. All rights reserved.
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页码：288 / 298
页数：11
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