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Topological transform of singular points?

  1. Oct 2, 2008 #1
    Are singular points necessarily mapped to singular points under topological transformations? A specific example would a 2-space deformation of a triangle to any closed string with no cross over points. Would the three singular points of the triangle be necessarily mapped to three singular points on the closed string?
     
    Last edited: Oct 2, 2008
  2. jcsd
  3. Oct 4, 2008 #2
    I'm not a professional mathematician or student. Nevertheless I believe I have a legitimate question and practical reasons for knowing the answer. My readings have thrown some light on the question but I would still appreciate an answer:

    A triangle is smoothly deformed to a closed loop string without cross over points in 2 space.

    Will the three singular points:

    1. Be necessarily be mapped to three singular points on the string?

    2. If not, can they be mapped to just one or two points on the string?

    I am not interested in annihilation techniques other "treatments" of singular points in topological transformations. I stongly suspect #2 is correct, but I would like confirmation.
     
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