On Simply-Connected 4-Manifolds
On Simply-Connected 4-Manifolds
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关于单连通 4 流形
DOI：
10.1112/jlms/s1-39.1.141
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发表时间：
1964
影响因子：
1.2
通讯作者：
C. Wall
中科院分区：
文献类型：
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作者：
C. Wall
本文讨论了闭的、定向的、微分的、单连通的4-流形的微分同胚分类(但没有成功地实现)。它源于观察(由于Pontrjagin和Milnor[2])，如果两个这样的流形Mx和M2在#2(JFT-)上有同构的交数的二次型，则存在映射/：M1-^-Mi，它是同伦等价的，并且从M2的切丛诱导出Mx的切丛(见下文)。同样的结果也是已知的，从Mx的i-余边线到M2[4]。这表明
This paper concerns (but does not succeed in performing) the diffeomorphism classification of closed, oriented, differential, simply-connected 4-manifolds. It arises out of the observation (due to Pontrjagin and Milnor [2]) that if two such manifolds Mx and M2 have isomorphic quadratic forms of intersection numbers on #2(Jft-), then there is a map / : M1-^-Mi which is a homotopy equivalence and induces the tangent bundle of Mx from that of M2 (see below). The same result is also known to follow from /i-cobordism of Mx to M2 [4]. This suggests