English

A note on rationally slice knots

Geometric Topology 2022-12-27 v1

Abstract

Kawauchi proved that every strongly negative amphichiral knot KS3K \subset S^3 bounds a smoothly embedded disk in some rational homology ball VKV_K, whose construction a priori depends on KK. We show that VKV_K is independent of KK up to diffeomorphism. Thus, a single 4-manifold, along with connected sums thereof, accounts for all known examples of knots that are rationally slice but not slice.

Keywords

Cite

@article{arxiv.2212.12951,
  title  = {A note on rationally slice knots},
  author = {Adam Simon Levine},
  journal= {arXiv preprint arXiv:2212.12951},
  year   = {2022}
}

Comments

9 pages, 2 figures

R2 v1 2026-06-28T07:52:22.152Z