English

Equivariantly slicing strongly negative amphichiral knots

Geometric Topology 2024-04-24 v1

Abstract

We prove obstructions to a strongly negative amphichiral knot bounding an equivariant slice disk in the 4-ball using the determinant, Spinc-structures and Donaldson's theorem. Of the 16 slice strongly negative amphichiral knots with 12 or fewer crossings, our obstructions show that 8 are not equivariantly slice, we exhibit equivariant ribbon diagrams for 5 others, and the remaining 3 are unknown. Finally, we give an obstruction to a knot being strongly negative amphichiral in terms of Heegaard Floer correction terms.

Keywords

Cite

@article{arxiv.2109.01198,
  title  = {Equivariantly slicing strongly negative amphichiral knots},
  author = {Keegan Boyle and Ahmad Issa},
  journal= {arXiv preprint arXiv:2109.01198},
  year   = {2024}
}

Comments

20 pages, 6 figures

R2 v1 2026-06-24T05:38:37.807Z