AN EXAMPLE OF ANOMALOUS SINGULAR HOMOLOGY
AN EXAMPLE OF ANOMALOUS SINGULAR HOMOLOGY
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异常奇异同源性的一个例子
DOI：
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发表时间：
1962
期刊：
影响因子：
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通讯作者：
J. Milnor
中科院分区：
文献类型：
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作者：
M. Barratt;J. Milnor
导论.已知r维空间的切赫同调群在维数大于r时为零。我们将证明，相应的断言为奇异的同调群是假的，即使在范畴的局部（r 1）-连通的dogota。本文给出了一个r维紧X，它除了在一点处是局部可收缩的，使得具有有理系数的奇异同调群H，（X; Q）对q的无穷多个值都是非平凡的.这解决了Eilenberg和Steenrod提出的一个问题[1，问题22]。设X表示可数个r-球面（r > 1）的并集，它们有一个公共点和一个度量拓扑，使得球面的直径随着指数的增加而趋于零。这个例子是Steenrod提出的。我们的结果是
Introduction. The Cech homology groups of an r-dimensional space are known to vanish in dimensions greater than r. We will show that the corresponding assertion for the singular homology groups is false, even on the category of locally (r 1)-connected compacta. An rdimensional compactum X, locally contractible save at one point, is given such that the singular homology groups H,(X; Q) with rational coefficients are nontrivial for infinitely many values of q. This settles a question raised by Eilenberg and Steenrod [1, Problem 22]. Let X denote the union of a countable number of r-spheres (r > 1) with a single point in common and a metric topology such that the diameter of the spheres tends to zero with increasing index. This example was suggested by Steenrod. Our result is