English

One stabilization is not enough for closed knotted surfaces

Geometric Topology 2023-04-05 v1

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.

Keywords

Cite

@article{arxiv.2304.01504,
  title  = {One stabilization is not enough for closed knotted surfaces},
  author = {Kyle Hayden and Sungkyung Kang and Anubhav Mukherjee},
  journal= {arXiv preprint arXiv:2304.01504},
  year   = {2023}
}

Comments

7 pages, 4 figures, comments welcome

R2 v1 2026-06-28T09:48:14.457Z