Exceptional Dehn surgery on large arborescent knots

Ying-Qing Wu

Vol. 252 (2011), No. 1, 219–243

DOI: 10.2140/pjm.2011.252.219

Abstract

A Dehn surgery on a knot K in S³ 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.

Keywords

arborescent knots, exceptional Dehn surgery

Mathematical Subject Classification 2000

Primary: 57N10

Milestones

Received: 8 March 2010

Revised: 9 January 2011

Accepted: 12 January 2011

Published: 8 October 2011