On constraints for knots to admit chirally cosmetic surgeries and their calculations

Kazuhiro Ichihara; Tetsuya Ito; Toshio Saito

doi:10.2140/pjm.2022.321.167

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arXiv · 2112.04156

On constraints for knots to admit chirally cosmetic surgeries and their calculations

Kazuhiro Ichihara·Tetsuya Ito·Toshio Saito

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Abstract

We discuss various constraints for knots in $S^{3}$ to admit chirally cosmetic surgeries, derived from invariants of 3-manifolds, such as, the quantum $SO(3)$-invariant, the rank of the Heegaard Floer homology, and finite type invariants. We apply them to show that a large portion (roughly 75$\%$) of knots which are neither amphicheiral nor $(2,p)$-torus knots with less than or equal to 10 crossings admits no chirally cosmetic surgeries.

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Kazuhiro Ichihara, Tetsuya Ito, Toshio Saito. 2021-12-08. On constraints for knots to admit chirally cosmetic surgeries and their calculations. https://doi.org/10.2140/pjm.2022.321.167

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