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One stabilization is not enough for closed knotted surfaces

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arxiv 2304.01504 v1 pith:CHCPM76R submitted 2023-04-04 math.GT

Kyle Hayden , Sungkyung Kang , Anubhav Mukherjee This is my paper · ORCID
classification math.GT
keywords closedenoughknottedstabilizationsurfacesauckly-kim-melvin-ruberman-schwartzboundarybrief
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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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  1. Strong corks derived from the Akbulut cork

    math.GT 2026-01 conditional novelty 6.0 of 10

    The boundaries of the AKMR and Tange cork families, and nontrivial equivariant connected sums of them, are strong corks.

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