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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Sharland, Ayşe Altıntaş 2014. Examples of finitely determined map-germs of corank 2 from n-space to (n + 1)-space. International Journal of Mathematics, Vol. 25, Issue. 05, p. 1450044.


    Greuel, Gert-Martin and Le, Cong Trinh 2008. On deformations of maps and curve singularities. manuscripta mathematica, Vol. 127, Issue. 1, p. 1.


    Wall, C. T. C. 2008. Projection genericity of space curves. Journal of Topology, Vol. 1, Issue. 2, p. 362.


    Hernandes, M. E. Hernandes, M. E. Rodrigues and Ruas, M. A. S. 2007. $${\mathcal{A}}_e$$ -codimension of germs of analytic curves. manuscripta mathematica, Vol. 124, Issue. 2, p. 237.


    Millett, Kenneth C. and Rawdon, Eric J. 2003. Energy, ropelength, and other physical aspects of equilateral knots. Journal of Computational Physics, Vol. 186, Issue. 2, p. 426.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 117, Issue 2
  • March 1995, pp. 213-222

Looking at bent wires – -codimension and the vanishing topology of parametrized curve singularities

  • David Mond (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100073060
  • Published online: 24 October 2008
Abstract

Projecting a knot onto a plane – or, equivalently, looking at it through one eye – one sees a more or less complicated plane curve with a number of crossings (‘nodes’); viewing it from certain positions, some other more complicated singularities appear. If one spends a little time experimenting, looking at the knot from different points of view, then provided the knot is generic, one can convince oneself that there is only a rather short list of essentially distinct local pictures (singularities) – see Fig. 3 below. All singularities other than nodes are unstable: by moving one's eye slightly, one can make them break up into nodes. For each type X the following two numbers can easily be determined experimentally:

1. the codimension in ℝ3 of the set View(X) of centres of projection (viewpoints) for which a singularity of type X appears, and

2. the maximum number of nodes n into which the singularity X splits when the centre of projection is moved.

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[18]K. Saito . Quasihomogene isolierte Singularitäten von Hyperflächen. Invent. Math. 14 (1971), 123142.

[19]C. T. C. Wall . Finite determinacy of smooth map-germs. Bull. London Math. Soc., 13 (1981) 481539.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
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