Not all knots are smoothly round handle slice
Geometric Topology
2025-07-24 v1
Abstract
Freedman and Krushkal showed that if the surgery conjecture and the -cobordism conjecture hold for all topological 4-manifolds, then every link with pairwise zero linking numbers is topologically round handle slice. Kim, Powell, and Teichner showed that every knot is topologically round handle slice. We show that infinitely many knots fail to be smoothly round handle slice.
Keywords
Cite
@article{arxiv.2507.17584,
title = {Not all knots are smoothly round handle slice},
author = {Tye Lidman and Allison N. Miller and Arunima Ray},
journal= {arXiv preprint arXiv:2507.17584},
year = {2025}
}
Comments
4 pages, 4 figures