Unknotting number, ribbon concordance, and singular instantons
arXiv:2607.12768
The authors apply equivariant singular instanton Floer theory equipped with a Chern–Simons filtration to prove that unknotting sequences for many slice knots obtained via ribbon concordance must involve both positive and negative twists, and they extend the method to obstruct certain homology 3‑spheres from being surgery on a knot, supporting monotonicity of the Dehn surgery number under ribbon homology cobordism.
Abstract
We use equivariant singular instanton Floer theory with the Chern--Simons filtration to obstruct same-sign unknotting operations. We show that, for a large class of slice knots obtained through ribbon concordance, any unknotting sequence of null-homologous twists must contain both signs. The same method gives a --manifold analogue, obstructing certain homology --spheres from surgery on a knot and providing evidence for the monotonicity of the Dehn surgery number under ribbon homology cobordism.
15 pages