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May 4, 2012 at 11:18 comment added Fernando Muro Sorry, I don't know of a reference, but using algebraic models is very easy. Let's say DGL algebras, so as not to exclude the rational spaces with infinite-dimensional homotopy groups. The suspension of a DGL algebra whose underlying Lie algebra is free can be easily seen to have trivial differentials, since in the cilinder all diferentials are supported by the boundary, hence the claim follows.
May 4, 2012 at 2:00 history asked Jeff Strom CC BY-SA 3.0