Cosmetic surgeries on knots in homology spheres and the Casson--Walker invariant

2025/06/03 by Ichihara, Kazuhiro, Jong, In Dae · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2506.02682

Abstract

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.

Citations

• Achiral 1-cusped hyperbolic 3-manifolds not coming from amphicheiral null-homologous knot complements
• Left-orderable, non-L-space surgeries on knots

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• Finiteness of purely cosmetic fillings

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