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We present a necessary condition for Dehn surgery on a knot in double-struck S sign3 to be cyclic which is based on the A-polynomial of the knot. The condition involves a width of the Newton polygon of the A-polynomial, and provides a simple method of computing a list of possible cyclic surgery slopes. The width produces a list of at most three slopes for a hyperbolic knot which contains no closed essential surface in its complement (in agreement with the Cyclic Surgery Theorem). We conclude with an application to cyclic surgeries along non-boundary slopes of hyperbolic mutant knots.

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Shanahan, Patrick D. “Cyclic Dehn Surgery and the A-Polynomial.” Topology and Its Applications, vol. 108, no. 1, Jan. 2000, pp. 7–36.

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