1. ## Homotopy Group Question

I'm working out a proof for topology:

If a topological space has a trivial fundamental group, can you establish that all higher homotopy groups of that same space are also trivial?

2. I found a resource online that said that all higher homotopy groups are trivial if the space is contractible, but can you say anything stronger? And how would you show this?

3. Originally Posted by joeyjoejoe
I'm working out a proof for topology:

If a topological space has a trivial fundamental group, can you establish that all higher homotopy groups of that same space are also trivial?
Hint: think about spheres ( $S^2$ in particular).