Splitting a 4-manifold with infinite cyclic fundamental group, revised
Splitting a 4-manifold with infinite cyclic fundamental group, revised
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分裂具有无限循环基本群的 4 流形，已修订
DOI：
10.1142/s0218216513500818
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发表时间：
2013
影响因子：
0.5
通讯作者：
Akio Kawauchi
中科院分区：
文献类型：
--
作者：
Nobuyuki Kato;Motoaki Watanabe;Yoshihiko Yamaura;Hiroaki Nakamura;河内明夫;橋本義武;岩瀬則夫;Norio Iwase;橋本義武;Akio Kawauchi
本文是作者早期关于具有无限循环基本群的闭连通定向4-流形的TOP-分裂的论文的修正版。证明了具有无限循环基本群的闭连通定向四维流形是TOP-分裂的，如果它是TOP-分裂的。由此，我们看到，如果交形式是不定的，则具有无限循环基本群的闭连通定向4-流形是TOP-分裂的。这也意味着每个具有无限循环基本群的闭连通定向光滑自旋4-流形是TOP-分裂的。
This article is a revised version of the author's earlier paper on a TOP-splitting of a closed connected oriented 4-manifold with infinite cyclic fundamental group. We show that a closed connected oriented 4-manifold with infinite cyclic fundamental group is TOP-split if it is virtually TOP-split. As a consequence, we see that a closed connected oriented 4-manifold with infinite cyclic fundamental group is TOP-split if the intersection form is indefinite. This also implies that every closed connected oriented smooth spin 4-manifold with infinite cyclic fundamental group is TOP-split.