The alternating-knot nonexistence conjecture for chirally cosmetic surgeries

Let $K$ be an alternating knot in $S^{3}$ that is non-amphicheiral and is not a $(2,p)$-torus knot. Alternating-knot nonexistence conjecture. The knot $K$ does not admit chirally cosmetic surgery. The paper describes this as a more plausible and tractable consequence of the broader classification conjecture; it remains open in general.