I have a little hard time understanding the definition of a simply connected space in terms of a fundamental group. A space is simply connected if its fundamental group is trivial, has only one element?(adsbygoogle = window.adsbygoogle || []).push({});

It's been some time since I played around with homotopy. My understanding is that a set of path homotopy classes of loops satisfies the axioms of a group.

Is one element of that group just one loop? If so, how does that tell you there is no holes the loop is encompassing. This where I get confused. Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Simply Connected and Fundamental Group

**Physics Forums | Science Articles, Homework Help, Discussion**