Cech上同调的单纯复形表示
The Simplicial Complex Representation of The Cech Cohomology
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摘要: 本文根据Cech上同调的相关知识和各学者对Cech上同调的定义,从代数的角度出发,利用单纯形方法对拓扑空间的Cech上同调进行讨论,通过构造函子,给出了Cech上同调的单纯复形表示,证明Cech上链复形就是一类特殊的单纯复形,从而Cech上同调是单纯上同调。Abstract: In this paper, based on the knowledge of the Cech cohomology and the definition of the Cech cohomology by various scholars, from the perspective of algebra, the simplicial method is used to discuss the Cech cohomology of topological space. By constructing the functor, the simplicial complex representation of the Cech cohomology is given, and it is proved that Cech complex is a special type of simplicial complex, so the Cech cohomology is the simplicial cohomology.