EXCEPTIONAL DEHN SURGERY ON LARGE ARBORESCENT KNOTS

A Dehn surgery on a knot K in S(3) is exceptional if it produces a reducible, toroidal or Seifert fibered manifold. It is known that a large arborescent knot admits no such surgery unless it is a type II arborescent knot. The main theorem of this paper shows that up to isotopy there are exactly three large arborescent knots admitting exceptional surgery, each of which admits exactly one exceptional surgery, producing a toroidal manifold.