Non-smoothable Four-manifolds with Infinite Cyclic Fundamental Group
Non-smoothable Four-manifolds with Infinite Cyclic Fundamental Group
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无限循环基本群的非光滑四流形
DOI：
10.1093/imrn/rnm031
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发表时间：
2007
影响因子：
1
通讯作者：
P. Teichner
中科院分区：
文献类型：
--
作者：
Stefan Friedl;I. Hambleton;P. Melvin;P. Teichner
在[11]中，我们中的两个人构造了一个闭的定向四维流形，其基本群Z不分裂S1 × S3。在本说明中，我们表明，这4-流形，以及其他各种衍生自它，不承认光滑结构。此外，我们还找到了一个具有完全相同性质的4-流形的无限族。作为推论，我们得到了在任何有理同调球上都不是光滑切片的拓扑切片纽结。
In [11], two of us constructed a closed oriented 4-dimensional manifold with fundamental group Z that does not split off S1 × S3. In this note we show that this 4-manifold, and various others derived from it, do not admit smooth structures. Moreover, we find an infinite family of 4-manifolds with exactly the same properties. As a corollary, we obtain topologically slice knots that are not smoothly slice in any rational homology ball.