Arf invariants of strongly invertible knots obtained from unknotting number one knots (Q1804714)

It is well-known, that if \(k\) is a knot of unknotting number one, the double cover of \(S^3\) branched over \(k\) is a 3-manifold \(\Sigma_2(k)\); we can obtain \(\Sigma_2(k)\) by Dehn surgery on some knot \(C\) in \(S^3\). This paper produces an effective method to determine the Arf invariant \(\text{Arf}(C)\) by using the Conway polynomial \(\nabla_L(z)=\sum^\infty_{n=0} a_{2n}(k)z^{2n}\), where \(a_{2n}(k)=0\) except a finite number of \(n:\text{Arf}(C)=a_4(k)\pmod2\).