Exceptional Dehn surgery on large arborescent knots

Details Exceptional Dehn surgery on large arborescent knots Exceptional Dehn surgery on large arborescent knots

2006-10-27

arxiv.org/abs/math/0610871v1

Mathematics

Geometric Topology

Scientific paper

A Dehn surgery on a knot $K$ in $S^3$ is exceptional if it produces a reducible, toroidal or Seifert fibred 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.

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