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.
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