The third term in lens surgery polynomials. (English) Zbl 1472.57012
Summary: It is well-known that the second highest coefficient of the Alexander polynomial of any lens space knot in \(S^3\) is \(-1\). We show that if the third highest coefficient of the Alexander polynomial \(\Delta_K(t)\) of a lens space knot \(K\) in \(S^3\) is non-zero, then \(\Delta_K(t)\) coincides with the Alexander polynomial of the \((2,2g+1)\)-torus knot, where \(g\) is the Seifert genus of \(K\).
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