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Möbius bundle

  1. Nov 20, 2011 #1
    Hi,

    i can not understand how circle has a nontrivial bundle, Möbius bundle. Can you say me what is its transition function on it.
     
  2. jcsd
  3. Nov 20, 2011 #2

    lavinia

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    Gold Member

    multiplication by -1.

    Similarly the Klein bottle is reflection of a circle.

    A way to visualize the Klein bottle is to look at the transformation (x,y) -> ( x+ 1/2,-y) on the unit square viewed as the fundamental domain of the torus.
     
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