A couple weeks ago I assited a talk about Whitehead´s problem and there the speaker mentioned that such statement is equivalent to the next:
($\star$) Every abelian, compact (Hausdorff off course) and path-connected topological group is isomorphic (as a topological group) to some circles product.
I have been looking on internet but I can not find neither the equivalence nor the second statement itself.
Somebody knows where can I read about this and if there is some proof of ($\star$)'s consistency (and independence) that does not go trough Whitehead´s problem?
Thank you!