Comparing homologies: Cech's theory, singular chains, integral flat chains and integral currents
Comparing homologies: Cech's theory, singular chains, integral flat chains and integral currents
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比较同源性：切赫理论、奇异链、积分平链和积分电流
DOI：
10.4171/rmi/489
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发表时间：
2007
影响因子：
1.2
通讯作者：
T. Pauw
中科院分区：
文献类型：
--
作者：
T. Pauw
给出了S的一个定理的新证明。Mardesic，由G.E. Bredon，切赫和奇异的某些局部连通空间的同调群重合。我们利用整平链的链复形（H. Whitney）和积分电流（H.费德勒和W. H. Fleming）定义欧氏空间子集的新同调群。我们证明这些验证的公理Eilenberg和Steenrod，我们提供Lipschitz风味的地方连通性条件，保证这些群体与切赫的。这些理论之间的关系与许多几何变分问题的可解性和正则性有关。
We give a new proof of a Theorem of S. Mardesic, generalized by G.E. Bredon, that Cech and singular homology groups of certain locally connected spaces coincide. We use the chain complexes of integral flat chains (H. Whitney) and integral currents (H. Federer and W. H. Fleming) to define new homology groups of subsets of Euclidean space. We show these verify the axioms of Eilenberg and Steenrod, and we provide Lipschitz-flavored local connectedness conditions which guarantee these groups coincide with Cech's. Relations between these theories is relevant for the solvability and regularity of many geometric variational problems.