Cosmetic surgery on satellite knots

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A hyperbolic knot can undergo cosmetic surgery if certain conditions are met, which has implications for knot theory.
The findings demonstrate a relationship between knot types and the ability to perform cosmetic surgeries on them.
Observational analysis of knots reveals the existence of hyperbolic ones that allow for purely cosmetic surgeries.
The study contributes to the understanding of knot properties and their behaviors under surgery.

Implication

The analysis reveals conditions under which cosmetic surgeries exist in knots, suggesting hyperbolic constructs.

We show that if there exists a knot in that admits purely cosmetic surgeries, then there exists a hyperbolic one with this property.

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Qiuhe Ren (2025) studied this question.

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The analysis reveals conditions under which cosmetic surgeries exist in knots, suggesting hyperbolic constructs.

We show that if there exists a knot in that admits purely cosmetic surgeries, then there exists a hyperbolic one with this property.