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The fundamental group of the disk is trivial, why?

  1. Apr 1, 2009 #1
    How do we show that the fundamental group of the disk D^2={(x,y) in RxR: x^2 +y^2< or eq. to 1} is trivial?

    I know how to show that the fundamental group of the circle is isomorphic to the group of the integers under addition, but for some reason, I don't see a way to show that the fundamental group of the disk is trivial.
     
  2. jcsd
  3. Apr 1, 2009 #2

    Dick

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    Because the disk is contractible?
     
  4. Apr 2, 2009 #3
    Oh yes so there is a contraction and from there we can get a path homotopy that shows that every loop in the disk is path homotopic to the constant loop at the base point. Hence the fundamental group of the disk is trivial.
    Thanks
     
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