Isolated exceptional Dehn surgeries on hyperbolic knots

Abstract

For a hyperbolic knot in the 3-sphere, at most finitely many Dehn surgeries yield non-hyperbolic manifolds. Such exceptional surgeries are classified into four types, lens space surgery, small Seifert fibered surgery, toroidal surgery and reducing surgery, according to the resulting manifolds. For each of the three types except reducing surgery, we give infinitely many hyperbolic knots with integral exceptional Dehn surgeries of the given type, whose adjacent integral surgeries are not exceptional.