Vol. 252, No. 1, 2011

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ISSN: 0030-8730
Exceptional Dehn surgery on large arborescent knots

Ying-Qing Wu

Vol. 252 (2011), No. 1, 219–243
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
Authors
Ying-Qing Wu
Department of Mathematics
University of Iowa
14 MacLean Hall
Iowa City, IA 52242-1419
United States