This research finds that infinitely many knots do not conform to smooth round handle slice criteria, suggesting limits to existing knot theories.
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.
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Lidman et al. (2025) studied this question.
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