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Trivial fundemental group

  1. Nov 13, 2009 #1

    Could anyone help some up briefly what it means if the fundemental group of a space X is trivial.

    As i understand it: if the fundemental group is trivial, this telling us that there is only one class of loops, ie the constant loops or ones homotopic to constant loop.

    Is this right?

  2. jcsd
  3. Nov 14, 2009 #2
    Yes that is right. A great example to consider is [itex]\mathbb{R}^n[/itex] whose fundamental group is trivial.
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