Not all knots are smoothly round handle slice

2025/07/23 by Tye Lidman, Lidman, Tye, Allison N. Miller +3
Computer Science · #Artificial Intelligence in Games

paper · pdf · doi:10.48550/arxiv.2507.17584

Abstract

Freedman and Krushkal showed that if the surgery conjecture and the s-cobordism conjecture hold for all topological 4-manifolds, then every link with pairwise zero linking numbers is topologically round handle slice. Kim, Powell, and Teichner showed that every knot is topologically round handle slice. We show that infinitely many knots fail to be smoothly round handle slice.

Citations

• The round handle problem
• Four-ball genus bounds and a refinement of the Ozsvath-Szabo tau-invariant
• Cosmetic surgeries on knots in S³
• Absolutely Graded Floer homologies and intersection forms for four-manifolds with boundary

Related

• The round handle problem
• Topologically slice (1,1)-knots which are not smoothly slice
• Ribbon concordances and slice obstructions: experiments and examples
• Knots and 4-manifolds
• The Conway knot is not slice