Genus formula conjecture for lens space knots in \Sigma2,3,72,3,7

Let Kp,kK_{p',k} be any knot whose parameter (p,k)(p',k) occurs in the displayed table for lens space surgeries in Σ(2,3,7)\Sigma(2,3,7), and let gg' be the table's value in its gg' column. Genus formula conjecture. Its genus satisfies

g(Kp,k)=g+p+12.g(K_{p',k})=\frac{g'+p'+1}{2}.

The table supplies examples of lens space knots in Σ(2,3,7)\Sigma(2,3,7), and the conjecture predicts their genera from the tabulated data; the source does not state a resolution.

Sources & referencesView supporting material

Primary source

Motoo Tange, “Homology spheres yielding lens spaces”, arXiv:1805.03455 (2018).

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