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arXiv 2005.116962020-05math.GT

4-流形中的光滑非平凡且拓扑平凡的零同调曲面

Smoothly knotted and topologically unknotted nullhomologous surfaces in 4-manifolds

Rafael Torres

备注：: Suggestions from a referee are incorporated in v2. Changes include: added Thm B and a discussion of an invariant of Fintushen-Stern to discern the knotted 2-tori, modified proof of Lemma 1, and a new title. v3: To appear Annales de l'Institut Fourier

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AI总结：

本文利用不等价光滑结构，在4-流形中构造无穷多光滑互异但拓扑同伦的零同调曲面，并指出其拓扑边界为柄体。

摘要：

我们指出，近期关于不等价光滑结构的构造提供了一种制造程序，可在众多4-流形中产生无穷多对光滑互不同伦的零同调2-环面与球面。相应的无穷集合由拓扑同伦的曲面组成，这些曲面在若干情形下拓扑地界定一个柄体。

英文摘要：

We point out that recent constructions of inequivalent smooth structures yield a manufacturing procedure of infinite sets of pairwise smoothly non-isotopic nullhomologous 2-tori and spheres inside a myriad of 4-manifolds. The corresponding infinite set consists of topologically isotopic surfaces that topologically bound a handlebody in several instances.

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