Volume 9, issue 1 (2009)

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Lens space surgeries as A'Campo's divide knots

Yuichi Yamada

Algebraic & Geometric Topology 9 (2009) 397–428

It is proved that every knot in the major subfamilies of J Berge’s lens space surgery (ie, knots yielding a lens space by Dehn surgery) is presented by an L–shaped (real) plane curve as a divide knot defined by A’Campo in the context of singularity theory of complex curves. For each knot given by Berge’s parameters, the corresponding plane curve is constructed. The surgery coefficients are also considered. Such presentations support us to study each knot of lens space surgery itself and the relationship among the knots in the set of lens space surgeries.

Dedicated to Professor Takao Matumoto on the occasion of his 60th birthday.

Dehn surgery, lens space, plane curve
Mathematical Subject Classification 2000
Primary: 14H50, 57M25
Secondary: 57M27
Received: 29 October 2007
Revised: 10 February 2009
Accepted: 11 February 2009
Published: 6 March 2009
Yuichi Yamada
Department of Systems Engineering
University of Electro-Communications
1-5-1, Chofugaoka, Chofu
Tokyo 182-8585