Unknotting number, ribbon concordance, and singular instantons

Hayato Imori; JungHwan Park; Masaki Taniguchi

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arXiv · 2607.12768

Unknotting number, ribbon concordance, and singular instantons

Hayato Imori·JungHwan Park·Masaki Taniguchi

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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 $3$--manifold analogue, obstructing certain homology $3$--spheres from surgery on a knot and providing evidence for the monotonicity of the Dehn surgery number under ribbon homology cobordism.

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Hayato Imori, JungHwan Park, Masaki Taniguchi. 2026-07-14. Unknotting number, ribbon concordance, and singular instantons. https://arxiv.org/abs/2607.12768

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