Cyclic Dehn surgery and the A-polynomial
The author investigates Dehn surgery on a knot in \(S^3\), i.e., the space resulting from sewing a solid torus along the boundary of a deleted regular neighborhood of a knot. The author applies a knot invariant introduced by \textit{D. Cooper, M. Culler, H. Gillet, D. D. Long} and \textit{P. B. Shalen} [Invent. Math. 118, No. 1, 47-84 (1994; Zbl 0842.57013)] called the \(A\)-polynomial. The main result provides a necessary condition for Dehn surgery to be cyclic. It is based on the width of the Newton polygon of the \(A\)-polynomial. The width produces a list of at most three slopes for a hyperbolic knot which contains no closed surface in its complement.
scientific article; zbMATH DE number 1538672