One stabilization is not enough for closed knotted surfaces

Kyle Hayden; Sungkyung Kang; Anubhav Mukherjee

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arXiv · 2304.01504

One stabilization is not enough for closed knotted surfaces

Kyle Hayden·Sungkyung Kang·Anubhav Mukherjee

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Abstract

In this brief note, we show that there exist smooth 4-manifolds (with nonempty boundary) containing pairs of exotically knotted 2-spheres that remain exotic after one (either external or internal) stabilization. It follows that the ``one is enough'' theorem of Auckly-Kim-Melvin-Ruberman-Schwartz does not hold for closed surfaces whose homology classes are characteristic.

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Kyle Hayden, Sungkyung Kang, Anubhav Mukherjee. 2023-04-04. One stabilization is not enough for closed knotted surfaces. https://arxiv.org/abs/2304.01504

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