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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年10月24日

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  • Kazuhiro Ichihara,
  • In Dae Jong

摘要

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.