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Homeomorphic Vs. Isotopic

  1. Dec 6, 2005 #1
    What is the difference?
  2. jcsd
  3. Dec 6, 2005 #2
    Don't you mean "homeomorphic vs isotropic"?
    The root words mean "same form" and "same change" (same difference?). Why not look them up in a scientific dictionary or on Google?
    (I looked them up. Never mind, sorry!)
    Last edited: Dec 7, 2005
  4. Dec 7, 2005 #3
    An isotopy is a smooth path of embeddings between two manifolds, while a homeomorphism is just a single function between two manifolds. Ie., a right circular cylinder centered at the origin with unit radius is a representation of an isotopy between the two circles at either end.
    While the unlink of 2 components is homeomorphic to the Hopf link, the two are not isotopic.
    Last edited: Dec 7, 2005
  5. Dec 7, 2005 #4
    So, it is appropriate to say:

    If two knot projections can be deformed into each other via a sequence of Reidemeister moves then the knot projections are isotopic to one another.
  6. Dec 7, 2005 #5
    Yep. Each Reidemeister move produces an isotopic projection of a knot with respect to the original.
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