Purely cosmetic surgeries and Casson--Walker--Lescop invariants

Kazuhiro Ichihara; In Dae Jong; Yasuyoshi Tsutsumi

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arXiv · 2603.11720

Purely cosmetic surgeries and Casson--Walker--Lescop invariants

Kazuhiro Ichihara·In Dae Jong·Yasuyoshi Tsutsumi

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Abstract

Using the rational surgery formula for the Casson--Walker--Lescop invariant of links in the $3$-sphere, we show that any null-homologous knot in a rational homology sphere admits at most two pairs of integral purely cosmetic surgeries. We also present constraints for null-homologous knots in certain $3$-manifolds with the first Betti number one or two to admit purely cosmetic surgeries. As another application, we show that, for a null-homologous knot in some $3$-manifolds, including $S^2 \times S^1$, there are at most two knots which are inequivalent to the given one, but whose exteriors are orientation-preservingly homeomorphic to that of the given one.

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BibTeX RIS

Kazuhiro Ichihara, In Dae Jong, Yasuyoshi Tsutsumi. 2026-03-12. Purely cosmetic surgeries and Casson--Walker--Lescop invariants. https://arxiv.org/abs/2603.11720

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