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?

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- Mar 1st 2009, 12:58 PMjoeyjoejoeHomotopy 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? - Mar 2nd 2009, 06:09 AMjoeyjoejoe
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?

- Mar 2nd 2009, 01:12 PMOpalg
Hint: think about spheres ($\displaystyle S^2$ in particular).