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Splitting a 4-manifold with infinite cyclic fundamental group, revised in a definite case

Akio Kawauchi

Osaka City University Advanced Mathematical Institute, Sugimoto Sumiyoshi-ku Osaka 558-8585, Japan

https://doi.org/10.1142/S0218216514500291Cited by:0 (Source: Crossref)

Abstract

A sufficient condition that a closed connected definite 4-manifold with infinite cyclic fundamental group is TOP-split is given. By this condition, it is shown that every closed connected definite smooth 4-manifold with infinite cyclic fundamental group is TOP-split. By combining with an earlier result, it is confirmed that every closed connected oriented smooth 4-manifold with infinite cyclic fundamental group is TOP-split. This also implies that every smooth sphere-knot in a closed simply connected smooth 4-manifold is topologically unknotted if the fundamental group of the complement is infinite cyclic.

Keywords:

AMSC: 57M10, 57M35, 57M50, 57N13

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