manuscripta mathematica

, Volume 93, Issue 1, pp 29–37 | Cite as

There are infinitely many Lissajous knots

  • Christoph Lamm


Convex Polyhedron Prime Integer Alexander Polynomial Seifert Surface Load Balance Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Bogle, M.G.V./Hearst, J.E./Jones, V.F.R./Stoilov, L.:Lissajous knots, J. Knot Theory and Ramifications3, no. 2, 121–140 (1994).zbMATHCrossRefGoogle Scholar
  2. [2]
    Burde, G./Zieschang, H.:Knots, de Gruyter (1985).Google Scholar
  3. [3]
    Eisenbud, D./Neumann, W.:Three-dimensional link theory and invariants of plane curve singularities, Annals of Mathematical Studies110, Princeton University Press (1985).Google Scholar
  4. [4]
    Ewing, B./Millet, K.C.:A load balanced algorithm for the calculation of the polynomial knot and link invariants (in: The mathematical heritage of C.F. Gauss; Collect. Pap. Mem. C.F. Gauss), 225–266 (1991).Google Scholar
  5. [5]
    Hartley, R./Kawauchi, A.:Polynomials of amphicheiral knots, Math. Ann.243, 63–70 (1979).zbMATHCrossRefGoogle Scholar
  6. [6]
    Jones, V.F.R./Przytycki, J.H.:Lissajous knots and billiard knots, to appear in Banach Center Publications.Google Scholar
  7. [7]
    Kauffman, L.H.:On knots, Annals of Mathematical Studies115, Princeton University Press (1987).Google Scholar
  8. [8]
    Lamm, C.:Lissajous-Knoten, Diplom thesis, Bonn (1996).Google Scholar
  9. [9]
    Murasugi, K.:On periodic knots, Comment. Math. Helv.46, 162–174 (1971).zbMATHCrossRefGoogle Scholar
  10. [10]
    Murasugi, K./Przytycki, J.H.:An index of a graph with applications to knot theory, Memoirs of the American Math. Soc.106 (1993).Google Scholar
  11. [11]
    Seifert, H.:On the homology invariants of knots, Quart. J. Math. Oxford (2),1, 23–32 (1950).zbMATHCrossRefGoogle Scholar
  12. [12]
    Traczyk, P.:Non-trivial negative links have positive signature, Manuscripta Math.61, 279–284 (1988).zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Christoph Lamm
    • 1
  1. 1.Konrad-Adenauer-Platz 3BonnGermany

Personalised recommendations