# Homotopy Group Question

• March 1st 2009, 12:58 PM
joeyjoejoe
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?
• March 2nd 2009, 06:09 AM
joeyjoejoe
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?
• March 2nd 2009, 01:12 PM
Opalg
Quote:

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).