English

Non-surjective satellite operators and piecewise-linear concordance

Geometric Topology 2021-07-22 v2

Abstract

We exhibit a knot PP in the solid torus, representing a generator of first homology, such that for any knot KK in the 3-sphere, the satellite knot with pattern PP and companion KK is not smoothly slice in any homology 4-ball. As a consequence, we obtain a knot in a homology 3-sphere that does not bound a piecewise-linear disk in any homology 4-ball.

Keywords

Cite

@article{arxiv.1405.1125,
  title  = {Non-surjective satellite operators and piecewise-linear concordance},
  author = {Adam Simon Levine},
  journal= {arXiv preprint arXiv:1405.1125},
  year   = {2021}
}

Comments

Published version; corrected errors from previous version. 40 pages; 12 figures, some in color

R2 v1 2026-06-22T04:06:47.876Z