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math.GT2026
Purely cosmetic surgeries on knots with low-span Jones polynomials, II
Kazuhiro Ichihara, Kengo Kishimoto
We show that a knot in the 3-sphere with a nontrivial Jones polynomial of span at most 14 admits no purely cosmetic surgery. This extends a result of the first author for span at m…
math.GT2026
Purely cosmetic surgeries on knots with low-span Jones polynomials
Kazuhiro Ichihara
In this paper, we show that a knot with a nontrivial Jones polynomial of span at most 11 does not admit purely cosmetic surgery.
math.GT2026
Purely cosmetic surgeries and Casson--Walker--Lescop invariants
Kazuhiro Ichihara, In Dae Jong, Yasuyoshi Tsutsumi
Using the rational surgery formula for the Casson--Walker--Lescop invariant of links in the -sphere, we show that any null-homologous knot in a rational homology sphere admits a…