This research reveals constraints for cosmetic surgeries on knots in homology spheres, suggesting implications for the Casson-Walker invariant.
We study cosmetic surgeries on a knot in a homology sphere. Several constraints on knots and surgery slopes to admit such surgeries are given. Our main ingredient is the rational surgery formula of the Casson--Walker invariant for 2-component links in the 3-sphere.
No takes yet. Share an insight, caveat, or question.
Ichihara et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: