Classification problems in differential topology—VI: Classification of (s −1)-connected (2s+1)-manifolds
Classification problems in differential topology—VI: Classification of (s −1)-connected (2s+1)-manifolds
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微分拓扑中的分类问题—VI：(s -1)-连通(2s+1)-流形的分类
DOI：
10.1016/0040-9383(67)90020-1
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发表时间：
1967
期刊：
影响因子：
--
通讯作者：
C. Wall
中科院分区：
文献类型：
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作者：
C. Wall
本文首先完成了几乎闭合(s-I)-连通(2s-t-I)-流形P的微分同态分类，并计算了这些P模的Grothendieck群9zs+ l，这些P模是由柄体边界得到的。P的边界的微分同胚类只依赖于92 ' I中的P的类，它的阶数最多为8。我们给出了这一结果的应用，并给出了Yzs+ l作为协配群的解释。在最后一节中，我们将外来球体的信息与Milnor的构造进行比较。
IN THIS paper we first complete the diffeomorphism classi6cation of almost-closed (s-I)-connected (2s-t-I)-manifolds P. We compute the Grothendieck group 9zs+ l of such P modulo as those obtained from boundaries of handlebodies. The diffeomorphism class of the boundary of P depends only on the class of P in 92” I, which has order at most 8. We give applications of this result, and an interpretation of Yzs+ l as a cobordism group. In a final section, we compare our information on exotic spheres with a construction due to Milnor.