Classification of Certain 6-Manifolds
Classification of Certain 6-Manifolds
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某些 6 流形的分类
DOI：
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发表时间：
1977
期刊：
影响因子：
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通讯作者：
G. Andrus
中科院分区：
文献类型：
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作者：
G. Andrus
0.导论.在（13）中，Wall将所有闭的、定向的、光滑的（或PL）6-流形分类为自同构、PL-同胚、拓扑同胚和同伦等价，这些流形具有无挠同调和零第二Stiefel-Whitney类。本文将这些分类推广到所有闭的、定向的、1-连通的、具有挠自由同调的拓扑6-流形。该方法不同于（13），但使用了沃尔分类的两种特殊情况。我们将在光滑、PL、拓扑流形和映射以及“流形”、“同胚”等范畴中工作，在这些类别中的任何一个都应该得到一致的解释。我感谢皇家欧洲方案研究金协会，在其任期内开展了本文所述的工作。
0. Introduction. In (13) Wall classified up to diffeomorphism, PL-homeomorphism, topological homeomorphism, and homotopy equivalence all closed, oriented, 1connected smooth (or PL) 6-manifolds with torsion-free homology and vanishing second Stiefel-Whitney class. This paper extends these classifications to all closed, oriented, 1-connected topological 6-manifolds with torsion-free homology. The method differs from that of (13) but uses two special cases of Wall's classification. We shall work in the categories of smooth, PL, and topological manifolds and maps, and 'manifold', 'homeomorphism', etc., are to be interpreted consistently in any one of these categories. I am grateful to the Royal Society for a Fellowship in the European Programme, during the tenure of which the work described in this paper was carried out.