Shrinking cell-like decompositions of manifolds. Codimension three
Shrinking cell-like decompositions of manifolds. Codimension three
复制标题
流形的收缩细胞状分解。
DOI：
10.2307/1971245
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发表时间：
1979
影响因子：
4.9
通讯作者：
J. Cannon
中科院分区：
文献类型：
--
作者：
J. Cannon
欧几里得 n 空间 En，n > 5，具有以下简单的不相交盘属性：En 中的奇异二维盘可以稍微调整以使其不相交。我们证明，对于流形的一大类细胞状分解，分解空间中的这种性质足以使分解空间成为流形。由此我们推导出R.D.爱德华兹在大量案例中证明的双悬置定理：任何同调球的双悬置都是拓扑球。我们还获得了爱德华兹流形因子定理的全面概括；爱德华兹定理指出，如果 X 是欧几里德 n 维空间 En 中的单细胞集合，则 (En/X) x E = En+l。
Euclidean n-space En, n > 5, has the following simple DISJOINT DISK PROPERTY: singular 2-dimensional disks in En may be adjusted slightly so as to be disjoint. We show that for a large class of cell-like decompositions of manifolds this property in the decomposition space is sufficient in order that the decomposition space be a manifold. As a consequence we deduce the DOUBLE SUSPENSION THEOREM proved in a large number of cases by R. D. Edwards: The double suspension of any homology sphere is a topological sphere. We also obtain a sweeping generalization of Edwards' MANIFOLD FACTOR THEOREM; Edwards' theorem states that, if X is a single cell-like set in Euclidean n-dimensional space En, then (En/X) x E = En+l.