Lens space surgeries as A’Campo’s divide knots

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.

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Keywords

Dehn surgery, lens space, plane curve

Mathematical Subject Classification 2000

Primary: 14H50, 57M25

Secondary: 57M27

References

Publication

Received: 29 October 2007

Revised: 10 February 2009

Accepted: 11 February 2009

Published: 6 March 2009

Authors

Yuichi Yamada
Department of Systems Engineering University of Electro-Communications 1-5-1, Chofugaoka, Chofu Tokyo 182-8585 JAPAN
http://mathweb.e-one.uec.ac.jp/~yyyamada/

Volume 9, issue 1 (2009)

Yuichi Yamada

Abstract