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

Kazuhiro Ichihara; In Dae Jong

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arXiv · 2506.02682

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

Kazuhiro Ichihara·In Dae Jong

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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.

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BibTeX RIS

Kazuhiro Ichihara, In Dae Jong. 2025-06-03. Cosmetic surgeries on knots in homology spheres and the Casson--Walker invariant. https://arxiv.org/abs/2506.02682

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