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October 20, 2025Open Access

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

Key Points

Cosmetic surgeries are constrained by specific requirements concerning knots and surgery slopes.
Key findings involve the application of the rational surgery formula of the Casson-Walker invariant to 2-component links.
The study examines how these properties interact within the context of homology spheres.
Understanding these surgeries may provide insights into topological properties of knots in three-dimensional spaces.

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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Cite This Study

Ichihara et al. (Tue,) studied this question.

synapsesocial.com/papers/68f6196ee0bbbc94fac3622d https://doi.org/https://doi.org/10.48550/arxiv.2506.02682