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Planar knots in 4-D

  1. Jul 19, 2004 #1
    Do conventional knots of linear strands in three dimensions have an analog which utilizes closed planar surfaces to form "knots" within four dimensional space, or in general closed N-dimensional manifolds to form "knots" within (N+2) dimensional space?

    Perhaps they could have applications to superstrings.
  2. jcsd
  3. Jul 21, 2004 #2

    matt grime

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    yes, look for ribbon groups, and so on. they are of use in quantum field theory stuff and branes and so on, and often fall under the title of quantum groups.
  4. Jul 21, 2004 #3
    Right on, Matt!
  5. Jul 21, 2004 #4


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    Isn't this like the Moebius Strip? If the strip isn't just a strip, but actually an infinite plane, then you have to have 4-D to keep it from intersecting itself.
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