On hyperbolic knots with Seifert fibered Dehn surgeries

Abstract

J.C. Dean has described a construction which produces knots having a small Seifert fibered manifold Dehn surgery. We translate this construction to tangles, and show that a trivializable tangle satisfies certain conditions if and only if the corresponding covering knot satisfies Dean's conditions. This can be used to show that all known examples of hyperbolic knots producing Seifert fibered manifolds, which were constructed by Montesinos's trick, can in fact be obtained by Dean's construction. We extend Dean's construction slightly, in order to include surgeries producing Seifert fibered manifolds with orbit surface a projective plane and two exceptional fibers, and we show an infinite family of hyperbolic knots having that kind of surgery.