Cyclic Dehn surgery and the A-polynomial

✍ Scribed by Patrick D. Shanahan

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 294 KB
• Volume: 108
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00117-0

✦ Synopsis

We present a necessary condition for Dehn surgery on a knot in S 3 to be cyclic which is based on the A-polynomial of the knot. The condition involves a width of the Newton polygon of the Apolynomial, 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.