Excluding cosmetic surgeries on hyperbolic 3-manifolds
arxiv(2024)
摘要
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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