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arXiv · 2403.10448

Excluding cosmetic surgeries on hyperbolic 3-manifolds

David Futer·Jessica S. Purcell·Saul Schleimer
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Abstract

This paper employs knot invariants and results from hyperbolic geometry to develop a practical procedure for checking the cosmetic surgery conjecture on any given one-cusped manifold. This procedure has been used to establish the following computational results. First, we verify that all knots up to 19 crossings, and all one-cusped 3-manifolds in the SnapPy census, do not admit any purely cosmetic surgeries. Second, we check that a hyperbolic knot with at most 15 crossings only admits chirally cosmetic surgeries when the knot itself is amphicheiral. Third, we enumerate all knots up to 13 crossings that share a common Dehn fillings with the figure-8 knot. The code that verifies these results is publicly available on GitHub.

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David Futer, Jessica S. Purcell, Saul Schleimer. 2025-11-20. Excluding cosmetic surgeries on hyperbolic 3-manifolds. https://doi.org/10.20382/jocg.v16i1a19

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