What Does a Trivial Fundamental Group Indicate About Space X?

[andlook]

Hey,

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

As i understand it: if the fundamental 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

 

[rasmhop]

Yes that is right. A great example to consider is \mathbb{R}^n whose fundamental group is trivial.