Open Access
December 2002 Lissajous Curves as A'Campo Divides, Torus Knots and Their Fiber Surfaces
Hiroshi GODA, Mikami HIRASAWA, Yuichi YAMADA
Tokyo J. Math. 25(2): 485-491 (December 2002). DOI: 10.3836/tjm/1244208867


We present a new form of the fiber surface $F$ for links arising from isolated complex plane curve singularities, in particular, the torus knot $T(p, q)$, where $F$ is a smoothing of a long thin band which has as many clasp-singularities as the unknotting number of $T(p, q)$. As an application, we give a visual proof that the Lissajous curve $(\cos{p\theta}, \cos{q\theta})$ regarded as a divide corresponds to the torus link $T(p, q)$.


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Hiroshi GODA. Mikami HIRASAWA. Yuichi YAMADA. "Lissajous Curves as A'Campo Divides, Torus Knots and Their Fiber Surfaces." Tokyo J. Math. 25 (2) 485 - 491, December 2002.


Published: December 2002
First available in Project Euclid: 5 June 2009

zbMATH: 1029.57006
MathSciNet: MR1948678
Digital Object Identifier: 10.3836/tjm/1244208867

Rights: Copyright © 2002 Publication Committee for the Tokyo Journal of Mathematics

Vol.25 • No. 2 • December 2002
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