Trivial fundemental group

  • Thread starter andlook
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  • #1
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Hey,

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?

Thanks
 

Answers and Replies

  • #2
430
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Yes that is right. A great example to consider is [itex]\mathbb{R}^n[/itex] whose fundamental group is trivial.
 

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